Effects of phospholipid unsaturation on the bilayer nonpolar region : a molecular simulation study

Molecular dynamics simulations of two monounsaturated phosphatidylcholine (PC) bilayers made of 1-palmitoyl-2-oleoyl-PC (POPC; cis -unsaturated) and 1-palmitoyl-2-elaidoyl-PC (PEPC; trans -unsaturated) were carried out to investigate the effect of a double bond in the PC -chain and its conformation on the bilayer core. Four nanosecond trajectories were used for analyses. A fully saturated 1,2-dimyristoyl-PC (DMPC) bilayer was used as a reference system. In agreement with experimental data, this study shows that properties of the PEPC bilayer are more similar to those of the DMPC than to the POPC bilayer. The differences between POPC and PEPC bilayers may be attributed to the different ranges of angles covered by the torsion angles 10 and 12 of the single bonds next to the double bond in the oleoyl (O) and elaidoyl (E) chains. Broader distributions of 10 and 12 in the E chain than in the O chain make the E chain more flexible. In effect, the packing of chains in the PEPC bilayer is similar to that in the DMPC bilayer, whereas that in the POPC bilayer is looser than that in the DMPC bilayer. The effect of the cis -double bond on torsions at the beginning of the O chain ( 4 and 5) is similar to that of cholesterol on these torsions in a myristoyl chain. —Róg, T., K. Murzyn, R. Gurbiel, Y. Takaoka, A. Kusumi, and M. Pasenkiewicz-Gierula. Effects of phospholipid unsaturation on the bilayer nonpolar region: a molecular simulation study. J. Lipid Res. 2004. 45: 326–336. Supplementary key words phosphatidylcholine • cis double bond • trans double bond • skew conformation • chain packing Phospholipids with two asymmetric hydrocarbon chains, of which one is fully saturated in the position and the other is monocis or polycis -unsaturated in the position, are the most common in nature (1). Among monocis unsaturated phosphatidylcholines (PCs), 1-palmitoyl-2-oleoylPC (POPC) is the most abundant. In the past, phospholipids with trans -unsaturated hydrocarbon chains were believed to be rare in nature. They were found in photosynthetic membranes of higher plants (2) and algae (3) as well as in some marine bacteria (4). With advances in separation and quantification techniques, new trans -unsaturated lipids have been identified in membranes of prokaryotes (5) and algal chloroplasts (6). In membranes of gram-negative bacteria, the relative proportion of trans unsaturated lipids increases under physiologically stressful conditions, such as increased temperature (7), starvation and desiccation (8), and organic solvents (9). The increase of the trans -tocis ratio results from an enzymatically controlled direct cis trans isomerization that does not shift the position of the double bond and occurs only at the position of the glycerol moiety (7). The cis trans conversion in the bacterial membrane is believed to be a fast and inexpensive mechanism enabling the membrane to maintain constant fluidity (5). Experimental (10–13) and molecular modeling (14) studies of model membranes show that in the membrane, a double bond in the cis conformation located near the middle of the chain interferes with the hydrocarbon chain packing. This decreases the cooperativity of the chain interactions and causes a substantial decline in the main phase transition temperature (13, 15–18). The effect of a trans double bond on the main phase transition temperature of hydrocarbon chains is much weaker (13, 16, 18). A double bond present in a PC chain increases the lateral PC-PC spacing in the bilayer (13). Nevertheless, the order and reorientational motion of saturated and cis -unsaturated (19, 20) as well as trans -unsaturated (21) hydrocarbon chains in model membranes are similar. In contrast, the translational diffusion of lipids (21–23) as well as small lipid-soluble molecules (24, 25) is significantly lower in cis and trans -unsatuAbbreviations: DMPC, 1,2-dimyristoyl-phosphatidylcholine; E, elaidoyl; M, myristoyl; MD, molecular dynamics; O, oleoyl; PC, phosphatidylcholine; PEPC, 1-palmitoyl-2-elaidoyl-phosphatidylcholine; POPC, 1-palmitoyl-2-oleoyl-phosphatidylcholine; PSPC, 1-palmitoyl-2-stearoylphosphatidylcholine; RAF, reorientational autocorrelation function; RDF, radial distribution function; SA, surface area. 1 To whom correspondence should be addressed. e-mail: mpg@mol.uj.edu.pl Manuscript received 5 May 2003 and in revised form 24 October 2003. Published, JLR Papers in Press, November 1, 2003. DOI 10.1194/jlr.M300187-JLR200 by gest, on N ovem er 7, 2017 w w w .j.org D ow nladed fom

Phospholipids with two asymmetric hydrocarbon chains, of which one is fully saturated in the ␥ position and the other is monocis -or poly-cis -unsaturated in the ␤ position, are the most common in nature (1).Among mono-cisunsaturated phosphatidylcholines (PCs), 1-palmitoyl-2-oleoyl-PC (POPC) is the most abundant.In the past, phospholipids with trans -unsaturated hydrocarbon chains were believed to be rare in nature.They were found in photo-synthetic membranes of higher plants (2) and algae (3) as well as in some marine bacteria (4).With advances in separation and quantification techniques, new trans -unsaturated lipids have been identified in membranes of prokaryotes (5) and algal chloroplasts (6).In membranes of gram-negative bacteria, the relative proportion of transunsaturated lipids increases under physiologically stressful conditions, such as increased temperature (7), starvation and desiccation (8), and organic solvents (9).The increase of the trans -to-cis ratio results from an enzymatically controlled direct cis -trans isomerization that does not shift the position of the double bond and occurs only at the ␤ position of the glycerol moiety (7).The cis -trans conversion in the bacterial membrane is believed to be a fast and inexpensive mechanism enabling the membrane to maintain constant fluidity (5).
Among several reports on computer simulations of unsaturated PC bilayers (27)(28)(29)(30)(31)(32)(33)(34)(35)(36)(37)(38), cis -and trans -unsaturated bilayers were compared in two of them (27,36).In a Langevin dynamics simulation study, Pearce and Harvey (27) showed that structural and dynamic properties of PCs with a trans double bond are similar to those of saturated PCs, whereas PCs with a cis double bond behave differently.In a comparative molecular dynamics (MD) simulation study, Murzyn et al. (36) showed that numbers of inter-lipid interactions via water bridges and charge pairs in cis -and trans -unsaturated PC bilayers are similar and that both are smaller than in a saturated 1,2-dimyristoyl-PC (DMPC) bilayer.
Scarce experimental (10,39) and molecular modeling (40)(41)(42) studies of mixed-chain phospholipids indicate that in monocis -unsaturated chains, torsion angles of the single bonds next to the double bond are highly distributed around skew (120 Њ ), skew Ј (240 Њ ), and trans (180 Њ ) conformations.The estimated distribution of angles ranges from 90 to 175 Њ and Ϫ 90 to Ϫ 175 Њ for the skew and skew Ј conformations (10).This follows from the steric energy profile (41), which has two broad minima centered at Ϯ 110 Њ , a relatively narrow and low-energy barrier centered at 180 Њ , and a broad, higher energy barrier extending from Ϫ 60 Њ ( gauche Ϫ ) to 60 Њ ( gauche ϩ ) with a small maximum at 0 Њ .Thus, torsion angles of the single bonds next to the double bond are unlikely to have conformations from the range Ͻ gauche Ϫ to gauche ϩ Ͼ .Similar results were obtained from quantum mechanical calculations of two model compounds, each containing two cis -unsaturated bonds, as well as from MD simulations of the polycis -unsaturated docosahexaenoic chain (32).Molecular modeling calculations indicate that the gauche probability of the torsion angles second next to the cis double bond is higher than that in fully saturated chains (39,40).Both experimental (43) and molecular modeling (40) studies indicate that a single cis double bond in the phospholipid ␤ -chain has practically no effect on the fully saturated ␥ -chain.To our knowledge, the effects of the trans double bond in the ␤ -chain on the neighboring torsion angles or the ␥ -chain have not been determined either experimentally or from simulations.
The aim of the present MD simulation study was to determine the effect of PC monounsaturation and the conformation ( cis or trans ) of the double bond in the ␤ -chain on hydrocarbon chain order, packing, and dynamics in the membrane.Two PC bilayers were studied: POPC (monocis -unsaturated) and 1-palmitoyl-2-elaidoyl-PC (PEPC; monotrans -unsaturated) together with a third, DMPC (fully saturated), used as a reference system.It is true that a bilayer made of fully saturated 1-palmitoyl-2-stearoyl-PC (PSPC) would constitute a better reference system for the POPC and PEPC bilayers (the length of corresponding alkyl chains of the three lipids is the same), but there is a serious problem in doing this.Unfortunately, there are very few experimental data for a PSPC bilayer, and this makes the generation of a computer model for this bilayer uncertain and unreliable and therefore unsuitable as a comparison.By contrast, reliable data for the DMPC bilayer are available, making this a safe reference system for comparative studies.The much lower temperature of the main phase transition of DMPC compared with PSPC is an additional advantage for this choice, because the three bilayers are all now in the liquid crystalline phase at the physiological temperature of 37 Њ C. DMPC and POPC bilayers were simulated for 15 ns and the PEPC bilayer for 8 ns.Analyses of the trajectories generated in the MD simulations confirmed that the cis double bond (torsion ␤ 11) promotes the conformational variability of the neighboring torsion angles ( ␤ 10 and ␤ 12), consistent with both the experimental and MD simulation data.In addition, they showed that the trans double bond has a similar effect, although the range of angles that ␤ 10 and ␤ 12 assume is broader.Indeed, ␤ 10 and ␤ 12 of the oleoyl (O; cis ) chain cover angles between 60 and 300 Њ , whereas those of the elaidoyl (E; trans ) chain cover the whole range of angles, i.e., between 0 and 360 Њ .

Simulation systems
POPC, PEPC, and DMPC bilayers used in this study consisted of 72 (6 ϫ 6 ϫ 2) PC molecules.POPC and PEPC bilayers were hydrated with 1,922 water molecules; the DMPC bilayer was hydrated with 1,622 water molecules (in each bilayer, water constituted ‫%93ف‬ by weight).The structure, numbering of atoms, and torsion angles in POPC, PEPC, and DMPC molecules are shown in Fig. 1.
The ␤-chain of POPC and PEPC has one double bond between C9 and C10 (Fig. 1).In POPC, the double bond is in the cis conformation (O chain), and in PEPC, it is in the trans conformation (E chain), so the torsion angle for the double bond, ␤11, is 0Њ for POPC and 180Њ for PEPC.The ␤and ␥-chains of DMPC [myristoyl (M) chain] and the ␥-chain of POPC and PEPC are fully saturated.Details concerning the construction of the POPC and PEPC molecules and subsequently bilayers, as well as the initial simulations of these bilayers, were described in Murzyn et al. (36).Details concerning the DMPC bilayer were described in Pasenkiewicz-Gierula et al. (44,45).

Simulation parameters
For PCs, optimized potentials for liquid simulations (OPLS) parameters (46), and for water, TIP3P parameters (47), were used.The united-atom approximation was applied to the CH, CH 2 , and CH 3 groups of PCs.The atomic charges on head groups of DMPC, POPC, and PEPC were practically the same; details are given in Pasenkiewicz-Gierula et al. (45).Procedures for supplementing the original OPLS base with the missing parameters for the PC head group were described in Pasenkiewicz-Gierula et al. (45), and those for the ␤-chain sp2 carbon atoms were described in Murzyn et al. (36).

Simulation conditions
POPC and PEPC bilayers were simulated for 15 and 8 ns, respectively, initially using the MD AMBER 4.0 (48) and then (last 5 ns) AMBER 5.0 (49) packages.Three-dimensional periodic boundary conditions with the usual minimum image convention were used.The SHAKE algorithm (50) was used to preserve the bond lengths of the water molecule, and the time step was set at fined and implemented in the AMBER package (49) were imposed on the double bond to prevent cis-trans isomerization.As neither the POPC nor the PEPC bilayer contains charge molecules, a residue-based cutoff with a cutoff distance of 12 Å was used to calculate the nonbonded interactions.The list of nonbonded pairs was updated every 25 steps.Other computational details are given in Murzyn et al. (36).
The MD simulations were carried out at a constant pressure (1 atm) and at a temperature of 310 K (37ЊC), which is above the main phase transition temperature for the POPC (Ϫ5ЊC) (18), PEPC (26ЊC) (18), and DMPC (23ЊC) bilayers.The temperatures of the solute and solvent were controlled independently.Both the temperature and pressure of the systems were controlled by the Berendsen method (52).The relaxation times for temperatures and pressure were set at 0.4 and 0.6 ps, respectively.The applied pressure was controlled anisotropically, each direction being treated independently with the trace of the pressure tensor kept constant for 1 atm.The DMPC bilayer was simulated for 15 ns under similar MD simulation conditions (44,45).

RESULTS
Details concerning the equilibration and validation of POPC and PEPC bilayers were described in Murzyn et al. (36), and those concerning the DMPC bilayer were described in Pasenkiewicz-Gierula et al. (45).For the analyses described below, the last 4 ns fragments of the generated trajectories were used.Errors in the derived average values are standard error estimates obtained from the block-averaging procedure.Because the torsion angles ␤3 and ␥3 (Fig. 1) are not in well defined, stable conformations (trans or gauche) (53), when calculating conformation-related quantities, ␤3 and ␥3 as well as the third segmental vector were not considered.

Cross-sectional area per PC
The average surface area (SA) per PC is 64.3 Ϯ 0.6 Å 2 in POPC, 63.5 Ϯ 0.6 Å 2 in PEPC, and 60.2 Ϯ 0.6 Å 2 in DMPC bilayers.The values for the POPC and DMPC bilayers are in good agreement with those published in the literature.SA/PC in the POPC bilayer was estimated to be 63 Å 2 from POPC monolayer studies at the surface pressure of 30 mN/m (54) and 66 Å 2 at the surface pressure of 20 mN/m (55).For the DMPC bilayer, the best estimate for SA/PC is ‫06ف‬ Å 2 (56).For the PEPC bilayer, there are no published experimental data.

Molecular order parameter of PC alkyl chains
The molecular order parameter, S mol , profiles [for definition, see Róg and Pasenkiewicz-Gierula ( 53)] along the ␤and ␥-chains in the POPC, PEPC, and DMPC bilayers are shown in Fig. 2. Shapes of the profiles for the O and E chains agree well with those given in Seelig and Waespear evi (18).For the POPC ␥-chain, the S mol profile agrees with that of Holte et al. (43) and Seelig and Waespe-ar evi (18).As can be seen from Fig. 2, S mol profiles for ␤-chains as well as ␥-chains of POPC, PEPC, and DMPC are similar, except for segments 10 and 11 of the O chain (i.e., segments that include the cis double bond), for which S mol values are substantially lower.Average S mol values for the POPC and PEPC chains are only slightly lower than those for the DMPC chains (Table 1), so saturated, mono-cis-unsaturated, and mono-trans-unsaturated chains are similarly ordered.

Tilt of PC alkyl chains
The tilt angle of a PC chain as well as the ⌬ segment (C-C bonds 4-9 above the double bond) and the segment (C-C bonds 10-17 below the double bond) of the O and E chains were derived as shown in (Eq. 1) where is the angle between the bilayer normal and the average segmental vector (averaged over appropriate segmental vectors у 4) (the nth segmental vector links n Ϫ 1 and n ϩ 1 carbon atoms in the alkyl chain), and 〈 〉 denotes both the ensemble and the time average.The distributions of tilt angles of ␤and ␥-chains in the POPC, PEPC, and DMPC bilayers are shown in Fig. 3A, B and those of the ⌬ and segments are shown in Fig. 3C, D. Average tilts of the PC chains, given in Table 1, are similar in the three bilayers.Also, tilts of the ⌬ and segments are S ˆc ˆc ´S ˆc ˆc ´arccos similar in the POPC and PEPC bilayers, but in both bilayers, the ⌬ segment is significantly less tilted than the segment (Table 1).A large difference between the O and E chains is seen in distributions (Fig. 4) and average values (Table 1) of tilt angles of the double bonds.The average tilt of the cis double bond is 11Њ larger than that of the trans double bond, which, on the other hand, is similar to that of the single C9-C10 bond in the M chain.

Conformation of PC alkyl chains
Probability profiles of the gauche conformation for C-C bonds along the ␤and ␥-chains in the POPC, PEPC, and DMPC bilayers are shown in Fig. 5A, B (the gauche probability for the double bond is zero).The cis double bond has a strong effect on the torsion angles of single bonds at the beginning (␤4 and ␤5) and middle (␤9, ␤10, ␤12, and ␤13) of the ␤-chain.␤4 and ␤5 have significantly higher and lower gauche probabilities, respectively, than their counterparts in the fully saturated M chain.A similar ef-   fect was brought about in the DMPC ␤-chain by cholesterol (53).The gauche probability of ␤10 and ␤12 (next to the double bond) is zero, and that of ␤9 and ␤13 (second next to the double bond) is higher than that in the M chain.The trans double bond does not influence torsion angles at the beginning of the ␤-chain but, like the cis double bond, increases the gauche probability of ␤9 and ␤13, although to a lesser extent.The gauche probability for ␤10 and ␤12 in the E chain is nonzero but is distinctly lower than that in the M chain.The double bond (cis or trans) has practically no effect on the gauche probability along the ␥-chain.
Populations of conformations of torsion angles that are first (␤10 and ␤12) and second (␤9 and ␤13) neighbors of the double bond in the POPC and PEPC bilayers are illustrated in Fig. 6. ␤9 and ␤13 of both the O and E chains assume discrete low-energy conformations (trans or gauche) in 99% of cases (Fig. 6A, B, G, H), whereas ␤10 and ␤12 of both the O and E chains continuously populate angles between 60 and 300Њ and 0 and 360Њ, respectively, with an apparent single maximum at 180Њ (Fig. 6C-F).Detailed inspection reveals that the distributions of conformations of ␤10 and ␤12 in the O chain have shoulders indicating nonuniform populations of the angles.Indeed, time profiles of the ␤12 conformation in some cases have a bimodal character (Fig. 7A).
Correlations between values of torsion angles for pairs of angles neighboring the trans double bond in the PEPC bilayer are shown as contour plots in Fig. 8.For comparison, a contour plot for a pair of "typical" torsion angles (␥7 and ␥8) in the ␥-chain is also shown (Fig. 8A).For the ␥7-␥8 pair, five regions on the plot can be recognized, one for trans-trans conformations and four for trans-gauche conformations (Fig. 8A).Gauche-gauche conformations are much less populated, so they do not appear on the plot.
Torsion angles ␤10 and ␤12 do not reside in the lowenergy conformations typical for single C-C bonds; therefore, they cover different regions on the plot.For discrete trans, gauche ϩ , and gauche Ϫ conformations of ␤9 and ␤13, the values of ␤10 and ␤12 cover nearly the whole range of angles (Fig. 8B, C) (relatively less populated conformations do not appear on the plot).The contour plot for the ␤12-␤10 pair shows that conformations of these torsion angles are uncorrelated (Fig. 8D); the region covered on the plot is a simple superposition of these angle distributions (cf.Fig. 6D, F).Similar results were obtained for torsion angles next to the cis double bond (data not shown).

Conformation lifetimes
Figure 6C, D shows that ␤10 and ␤12 of the O and E chains have a nonzero probability to populate any angle in the range between 60 and 300Њ and 0 and 360Њ, respectively.This means that these torsion angles do not have stable conformations.Figure 7A, B well illustrates the instability of the conformational states of ␤12 in the O and E chains.Other single C-C bonds in PC hydrocarbon chains assume low-energy trans and gauche conformations, as illustrated in Fig. 7C.Lifetime profiles of these conformations along the ␤and ␥-chains in the POPC, PEPC, and DMPC bilayers are shown in Fig. 5C, D. Lifetimes of gauche conformations for POPC ␤10 and ␤12 were set to zero because these angles are never gauche.Lifetimes of trans conformations for POPC ␤10 and ␤12 as well as trans and gauche conformations for PEPC ␤10 and ␤12 are very  short, which indicates that these conformations are very unstable.For ␤9 and ␤13 of the O and E chains, lifetimes of the gauche conformation increase by the same amount relative to those of the M chain, whereas lifetimes of the trans conformation increase for ␤9 and ␤13 of only the E chain.This is the likely reason why the probability of gauche for ␤9 and ␤13 of the O chain is higher than that of the E chain (Fig. 5A).For torsion angles other than ␤9, ␤10, ␤12, and ␤13, lifetimes of both the trans and gauche conformations are similar in all three bilayers.

Chain packing in the hydrophobic core
Radial distribution functions (RDFs) calculated for the center of mass of the PC alkyl chains belonging to different PC molecules in the POPC, PEPC, and DMPC bilayers are shown in Fig. 9A.A broad first maximum and the lack of a second maximum in the RDF for the POPC bilayer indicate that the cis double bond disrupts a regular chain packing observed in the DMPC and PEPC bilayers (Fig. 9A).
The RDFs were decomposed into RDFs for the ␤-chains (a ␤-␤ RDF; Fig. 9B), ␤and ␥-chains (a ␤-␥ RDF; Fig. 9C), and ␥-chains (a ␥-␥ RDF; Fig. 9D).As indicated in Fig. 9B, saturated ␤-chains pack much better than unsaturated ␤-chains, but trans-unsaturated chains pack better than cisunsaturated chains.The ␥-␥ RDFs in Fig. 9D show that the ␥-chains in the DMPC and PEPC bilayers are arranged regularly, whereas the ␥-chains in the POPC bilayer are not.In contrast, as the ␤-␥ RDFs in Fig. 9D show, the arrangement of the unsaturated ␤-chains relative to ␥-chains in both the POPC and PEPC bilayers is more regular than that of the saturated ␤-chains relative to ␥-chains in the DMPC bilayer.One can conclude that in the vicinity of a cis-unsaturated ␤-chain in the POPC bilayer, there are mainly saturated ␥-chains, whereas in the DMPC bilayer, a ␤-chain is surrounded by ␤-chains and a ␥-chain is surrounded by ␥-chains.

Rotational diffusion
Reorientational autocorrelation functions (RAFs) were calculated for the Legendre polynomial P1 for ␤-chain and ␥-chain vectors (Fig. 10A, B) in the POPC, PEPC, and DMPC bilayers.The ␤-chain (␥-chain) vector is a vector linking the middle of the C21-C22 (C31-C32) bond (Fig. 1) and the center of gravity of the chain.The RAF curves could not be satisfactorily fitted to a sum of exponentials; thus, the results presented are only qualitative.The effect of the double bond on the alkyl chain rotation is weak, independent of the bond conformation.A similar conclusion was drawn from spin-label studies of bilayers made of saturated, cis-unsaturated, and trans-unsaturated PCs (21).In those studies, however, the effects of unsaturation on the chain reorientational motion were monitored indirectly via the reporter group of the spin-label molecule.

DISCUSSION
In our previous paper (36), no significant effect of the conformation (cis or trans) of the double bond in the PC ␤-chain was found on the organization of the bilayer-water interface.In this paper, details of the effect of the double bond and its conformation on the organization of the bilayer core were investigated.In the MD simulation study, properties of the hydrocarbon core of the mono-cisunsaturated (POPC), mono-trans-unsaturated (PEPC), and fully saturated (DMPC) bilayers were compared.
Average parameters characterizing monounsaturated PC bilayers in the liquid crystalline state obtained in this study are similar to those derived experimentally, in spite of the limited size of the computer models.In particular, the mean SA per PC in the POPC (and PEPC) bilayer of ‫46ف‬ Å 2 agrees with experimental estimates (54,55) and, as the experiments predict (13), is greater than that in the DMPC bilayer of ‫06ف‬ Å 2 .Profiles of the order parameter for the O and E chains have shapes similar to those obtained from NMR spectroscopy (18).In accord with the experimental data of Subczynski and Wisniewska (21), saturated, mono-cis-unsaturated, and mono-trans-unsaturated chains are similarly ordered, and as Holte et al. (43) showed, mono-cis-unsaturation in the ␤-chain has a minor effect on the order of the ␥-chain.
The effect of the cis double bond on the ␤4 and ␤5 torsions angles in the pure POPC bilayer is similar to that of cholesterol in the DMPC-cholesterol bilayer (53).In both bilayers, the gauche probability of the ␤4 is significantly higher and that of the ␤5 is significantly lower than the respective probabilities for the DMPC ␤-chain in the pure DMPC bilayer.This is a very interesting but puzzling result, because in the first case, the effect is caused by an intrinsic molecular factor, whereas in the second case, it is driven by intermolecular interaction.The changes in the gauche probability of ␤4 and ␤5 are most likely attributable to steric effects, but in the framework of the present study, their origin cannot be clearly indicated.Similar effects of the cis double bond and cholesterol may explain why water penetration through the POPC and DMPC-cholesterol bilayers is decreased similarly compared with that in the pure DMPC bilayer (26).The trans double bond has no effect on the ␤4 and ␤5 torsions angles.
Detailed conformational analyses of mono-and poly-cisunsaturated chains indicate that torsion angles of saturated C-C bonds next to the double bond have broad distributions around the skew, skewЈ, and trans conformations, with a low probability of conformations between gauche Ϫ and gauche ϩ (10,32,41).On the other hand, molecular mechanics calculations indicated that the gauche probability for the second next torsions to the double bond is higher than that in a fully saturated chain (39)(40)(41).To our knowledge, the effect of the mono-trans-unsaturated bond on the conformation of the neighboring single bonds has not been described in the literature.
Our MD simulation study demonstrated that both cis and trans double bonds strongly modify conformational states of the next (␤10 and ␤12) and second next (␤9 and ␤13) torsion angles.The distributions of ␤10 and ␤12 are continuous and broad, with maxima at 180Њ (Fig. 6).The range of angles covered by ␤10 and ␤12 depends on the conformation of the double bond.The values of ␤10 and  ␤12 in the O chain are between 60 and 300Њ (Fig. 6C, E), whereas in the E chain, they cover the whole range of angles between 0 and 360Њ (Fig. 6D, F).The result for the O chain is in accord with results from single crystal studies by Keneko, Yano, and Sato (10) and molecular mechanics calculations by Li et al. (41).The result for the E chain is an evidently new result of the present study; unfortunately, no experimental data are available to verify it.
Different ranges of angles covered by ␤10 and ␤12 in the O and E chains are the most likely explanation for the experimentally observed differences in the properties of the POPC and PEPC bilayers.A wider distribution of ␤10 and ␤12 in the E chain makes the chain more flexible.Moreover, the distribution of gauche rotamers along the E chain and the inclination of the C9ϭC10 bond are more similar to those of the M than of the O chain (Fig. 5A).Thus, the E chain is more adaptive than the O chain and, in many respects, displays properties similar to those of the M chain.This result is in agreement with the reported similarity in the subcell structure and the occurrence of polytypic structures of mono-trans-unsaturated and fully saturated fatty acid crystals (57).Also, it is in agreement with the conclusion drawn from experimental observation that cholesterol mixes well with saturated and mono-transunsaturated phospholipids but not with mono-cis-unsaturated phospholipids (24,58).
A greater similarity of the E chain to the M than to the O chain is also reflected in chain-chain RDFs (Fig. 9).The RDFs indicate that both mono-trans-unsaturated and fully saturated chains pack more regularly in the bilayer than the less adaptive mono-cis-unsaturated chains (Fig. 9A).Thus, the generally higher main phase transition temperatures of saturated and mono-trans-unsaturated bilayers than mono-cis-unsaturated bilayers may be attributed mainly to the observed differences in the chain packing.The RDFs shown in Fig. 9B, D indicate that, in contrast to the DMPC and PEPC bilayers, the ␤-chains as well as the ␥-chains in the POPC bilayer are not arranged regularly relative to each other.Nevertheless, spatial ordering of ␤-chains relative to ␥-chains is more apparent in the POPC and PEPC bilayers than in the DMPC bilayer (Fig. 9C).
Our MD simulation study confirmed an earlier Langevin dynamics simulation study of Pearce and Harvey (27) that showed that structural and dynamic properties of PCs with a trans double bond are similar to those of saturated PCs.Most likely, as a result of this similarity, phospholipids with trans-unsaturated hydrocarbon chains are much less abundant in nature than those with cis-unsaturated hydrocarbon chains.
In membranes of some bacteria, the relative proportion of trans-unsaturated fatty acids increases under physiologically stressful conditions (7)(8)(9).The increase results from an enzymatically controlled direct cis-trans isomerization of the double bond (7).Cis-trans isomerization was proposed as a biological mechanism of the regulation of bacterial membrane fluidity (5).The cis bond would increase fluidity, whereas the trans bond would decrease it.Unfortunately, experimental results (21)(22)(23) and the MD simulation results presented here do not support this hypothesis.
They indicate that the lateral self-diffusion of cis-unsaturated lipids in the bilayer is slower than that of trans-unsaturated lipids, whereas the rotational diffusion is similar.Furthermore, S mol profiles for cis-and trans-unsaturated chains have similar overall shapes.Thus, at temperatures above the main phase transition temperature for transunsaturated chains, the double bond in either the cis or the trans conformation has little effect on membrane fluidity and order.However, the biological role of cis-trans isomerization of the double bond in bacterial fatty acids might stem from differences in the interactions of other membrane components with cis-and trans-unsaturated chains.It has been demonstrated that membranes of bacteria living in extreme conditions contain polar carotenoids (59,60).Carotenoids and cholesterol have similar effects on alkyl chains of phospholipids (61,62) and both affect cisunsaturated chains less strongly than saturated chains (26,61,62); in the case of cholesterol, the effect is also less strong than that of trans-unsaturated chains (26).Because of the similarity of saturated and trans-unsaturated chains discussed above, one can expect that the effect of carotenoids on these chains is similar to that of cholesterol.Therefore, environmentally induced cis-trans isomerization of the double bond should result in a stronger effect of carotenoids (or similar molecules) on the hydrocarbon chains in the bacterial membrane whenever it contains carotenoid-like molecules.The structure of the lipid matrix of the membrane would then become more rigid and hydrophobic and thus less permeable for polar molecules and ions.In this way, bacterial cell membrane integrity would be better preserved and the cell could better sustain stressful external conditions.

CONCLUSIONS
This MD simulation study confirmed numerous experimental results, particularly that the order and rotational diffusion of mono-cis-unsaturated, mono-trans-unsaturated, and saturated chains do not differ significantly from one another.This study also confirmed both experimental and computer simulation results that torsion angles of saturated C-C bonds next to the cis double bond are broadly distributed (in the range between 60 and 300Њ) and the gauche probability for the second next torsions to the cis double bond is higher than in a fully saturated chain.
This study provided the following new results: (1) Torsion angles of saturated C-C bonds next to the trans double bond continuously populated the whole range of angles between 0 and 360Њ.This makes the mono-trans-unsaturated chain more adaptive than the mono-cis-unsaturated chain and in many respects similar to a fully saturated chain.(2) The intrinsic effect of the cis double bond on ␤4 and ␤5 torsions angles is very similar to the extrinsic effect of cholesterol on these angles in a fully saturated chain.Both in the POPC and DMPC-cholesterol bilayers, the gauche probability of ␤4 and ␤5 is much higher and lower, respectively, than that in the pure DMPC bilayer.
(3) The packing of the alkyl chains in a mono-trans-unsat-urated bilayer is similar to that in a saturated bilayer, whereas the packing of the alkyl chains in a mono-cisunsaturated bilayer is significantly looser.

Fig. 2 .
Fig. 2. Profiles of the molecular order parameter (S mol ) along the ␤-chain (A) and ␥-chain (B) in the POPC (closed squares), PEPC (closed triangles), and DMPC (closed circles) bilayers.The error bars indicate SEM.Average values of S mol are given in Table1.

Fig. 4 .
Fig. 4. Distribution of tilt angles of the double bond in the ␤-chain of POPC (thick line) and PEPC (dotted line).

Fig. 7 .
Fig. 7. Time profiles of conformations of the torsion angles ␤12 of arbitrarily chosen POPC (A) and PEPC (B) molecules and ␥12 of an arbitrarily chosen PEPC molecule (C).Trans, gauche ϩ , and gauche Ϫ are indicated at right as t, g ϩ , and g Ϫ , respectively.The dashed lines indicate the ranges of angles that characterize a given conformation.

Fig. 8 .
Fig. 8. Contour plots showing correlations between values of torsion angles for the pairs of angles ␥7 and ␥8 (A), ␤9 and ␤10 (B), ␤12 and ␤13 (C), and ␤10 and ␤12 (D) in the PEPC bilayer.In A, contours are plotted at intervals of 10, and in B-D, they are plotted at intervals of 2.

Fig. 9 .
Fig. 9. Radial distribution functions (RDFs) calculated for the centers of masses of the phosphatidylcholine (PC) alkyl chains belonging to different PC molecules for all chains (A), the ␤-chains relative to a ␤-chain (B), the ␤-chains relative to a ␥-chain (C), and the ␥-chains relative to a ␥-chain (D) in the POPC (thick line), PEPC (dotted line), and DMPC (thin line) bilayers.