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J. Phys. Chem. B 2009, 113, 92–102
Effects of Fatty Acid Inclusion in a DMPC Bilayer Membrane Gu¨nther H. Peters,*,†,§ Flemming Y. Hansen,† Martin S. Møller,†,§ and Peter Westh‡,§ Department of Chemistry, Technical UniVersity of Denmark, 2800 Kgs. Lyngby, Denmark; Department of Life Sciences and Chemistry, Roskilde UniVersity, 4000 Roskilde, Denmark; and MEMPHYS-Center for Biomembrane Physics ReceiVed: July 14, 2008; ReVised Manuscript ReceiVed: October 3, 2008
Free fatty acids in biomembranes have been proposed to be a central component in several cellular control and regulatory mechanisms. To elucidate some fundamental elements underlying this, we have applied molecular dynamics simulations and experimental density measurements to study the molecular packing and structure of oleic acid (HOA) and stearic acid (HSA) in fluid bilayers of dimyristoylphosphatidylcholine (DMPC). The experimental data show a small but consistent positive excess volume for fatty acid concentrations below 10 mol %. At higher concentrations the fatty acids mix ideally with fluid DMPC. The simulations, which were benchmarked against the densitometric data, revealed interesting differences in the structure and location of the fatty acids depending on their protonation status. Thus, the protonated (uncharged) acid is located rather deeply in the membrane with an average position of the carboxy group near the second carbon segment of the lipid chains with a typical end-to-end distance of 16-18 Å. This structure of the fatty acid brings about a rather tight lateral packing in the mixed membrane and a moderate ordering and hence stretching of the lipid chains. Deprotonation of the fatty acids is associated with a pronounced movement of their carboxy group to a more hydrated position at the membrane interface and a lateral expansion driven by the mutual repulsion of the anions. These changes increase both the disorder and the degree of interdigitation of the lipid chains, and they make the membrane thinner by 2-3 Å. Introduction Cell membranes are complex macromolecular assemblies of lipids and proteins that can exist in several physically different states depending on the membrane-constituting lipids, the inclusion of other molecules in the membrane, and environmental conditions.1-3 These factors regulate the physicochemical properties of membranes, such as structure, fluidity, permeability, or microdomain formation,4,5 and protein function, such as enzyme activity, protein-membrane interactions, or receptor binding.6-11 Lipids in biological membranes are usually maintained in the fluid (i.e., liquid-crystalline) state.12,13 Organisms generally have developed different mechanisms by which the physical state of the cell membrane can be changed to adopt to cellular response, thereby modulating intracellular signaling.14 Two effective mechanisms are based on adjusting the expression of cholesterol or fatty acyl composition of the lipids in cell membranes.15-17 For instance, bacteria that generally lack cholesterol have adapted a mechanism to maintain the membrane in a liquidcrystalline state by enzymatic modification of the fatty acyl composition of the membrane lipids.12,13,18-20 Typical modifications are shortening, branching, or desaturating of the fatty acid chains in the lipids, resulting in a lowering of the gel-to-liquidcrystalline phase transition temperature by up to 45 °C.21,22 Such compositional modification of membranes (known as homeoviscous adaptation23) is an efficient mechanism to maintain the correct membrane fluidity, thereby resisting for instance the deleterious impact of cold shock.23-28 * Corresponding author. E-mail:
[email protected]. † Technical University of Denmark. ‡ Roskilde University. § MEMPHYS - Center for Biomembrane Physics.
The levels of free fatty acids are usually low, but there are types, like the small intestine brush border membranes,29 where the free fatty acid content may reach 30% (w/w) of the total lipids.30-32 The level of free fatty acids in membranes is influenced by the diet; e.g. the Mediterranean diet, which is rich in oleic acid, leads to a higher concentration of oleic acid in various plasma membranes,33-35 and the diet has been associated with a reduced risk of developing cardiovascular and tumoral pathologies.36-40 In this context, synthetic derivatives of oleic acid have been used as anticancer and antihypertensive drugs, and it has been proposed that oleic acids have regulatory effects on membrane structure and membrane-embedded/associated signaling proteins.29 Similarly, polyunsaturated free fatty acids have been shown to perturb membrane lipid rafts, thereby affecting cell functions.41 Different amounts of saturated/ unsaturated free fatty acids in cells have also been utilized in cryoablative procedures.42 The amount of stearic acid relative to oleic and linoleic acids is greater in tissue from colonic adenocarcinoma than in normal colonic mucosa, and it has been proposed that the specific proportion of saturated and unsaturated fatty acids in different cancer types makes tumor cells more susceptible to cryo damage because the cell membranes containing relatively high levels of saturated fatty acid are transformed into the gel phase.42 The above outline suggests that free fatty acids (free FA) play a role in a diversity of membrane processes; yet the fundamental FA-lipid interactions which are underlying these biological effects are only sporadically investigated. We have therefore conducted both experimental and simulation studies to elucidate the effects of the inclusion of oleic acid and stearic acid in DMPC membranes. Since the protonation state (pKa) of fatty acids is very sensitive to charges in their local environment,10,43 we have performed molecular dynamics (MD) simula-
10.1021/jp806205m CCC: $40.75 2009 American Chemical Society Published on Web 12/15/2008
Molecular Packing of Fatty Acids in Bilayers tions of both the charged (sodium salt, hereafter referred to as NaFA) and uncharged (protonated, hereafter referred to as HFA) forms of respectively oleic acid (FA ) OA) and stearic acid (FA ) SA). In the experiments, we have used differential scanning calorimetry (DSC) to follow the gel-to-fluid transition temperature in the membrane as a function of the DMPC/FA composition and densiometry to determine the volume changes as a function of composition in order to get information about the packing in the DMPC/FA systems. The systems have only been simulated at one composition to limit the computation time, and the results have been validated by comparison to the experimental results. The simulations have also been used to extract information about effects on both the phospholipid structure and the FA structure as well as lipid packing in the membrane that are not available from the experimental results. These systems were chosen as they are experimentally manageable, and it is anticipated to capture some of the fundamental aspects of lipid/FA mixtures. Experimental Methods Materials. 1,2-Dimyristoyl-sn-glycero-3-phosphatidylcholine (DMPC, >99%) was purchased from Avanti Polar Lipids, Inc. (Alabaster, AL) in powder form and used without further purification. The fatty acids, cis-9-octadecenoic acid (oleic acid, HOA, 99%) and octadecanoic acid (stearic acid, HSA, 99%), were both purchased from Sigma-Aldrich (Steinheim, Germany). Sample Preparation. A key parameter for the analysis of the volumetric data is the precision to which the composition of the lipid suspensions is known. To achieve this, DMPC powder was initially hydrated in freshly made Milli-Q water (approximately 10 mL per 1 g DMPC). After repeated shaking and temperature cycling (∼10-40 °C) over at least 1 h, the homogeneous suspension was pipetted into ∼25 tarred glass vials (4 mL), closed with tight screw-caps and weighted to the nearest 0.01 mg. The glass vials were then freeze-dried for 48 h and weighed again. Small variations in the amounts of water adsorbed to the glass vials were taken into account by weighing a number of blanks (empty glass vials) also exposed to the freeze-drying procedure. The fatty acids were dissolved in chloroform:methanol (3:1) to a (precisely known) concentration of about 0.3 wt %. Then, enough fatty acid solution was added to a number of glass vials (each with about 45 mg of lyophilized DMPC) to produce FA mole fractions, xFA ) nFA/(nFA + nDMPC), in the range 0.05-0.30. The precise amount of fatty acid solution added was quantified by weight. The (dissolved) samples were thoroughly stirred and subsequently dried at room temperature in a nitrogen gas atmosphere. To remove traces of the organic solvent, the samples were kept at reduced pressure (0.02 mbar) and room temperature overnight. A parallel experiment with pure FA indicated that there was no loss of mass over a week when the sample was kept at vacuum. Hence, there was no detectable evaporation of FA in the process used to remove traces of residual organic solvent. The dry DMPC/ FA samples, along with a number of vials with pure DMPC (i.e., samples with xFA ) 0), were then hydrated with 1.6 mL of fresh Milli-Q water. Again, the hydrated sample was repeatedly shaken and temperature cycled and eventually exposed to a short (1 min) ultrasound treatment (Cole Palmer 8890 ultrasonic bath) to break up larger aggregates without producing small unilamellar vesicles. To test a possible dependence of the volume functions on the concentration of lipid, one experimental series was conducted with about 130 mg of lipid (precisely known) in the vials. All other steps in this series
J. Phys. Chem. B, Vol. 113, No. 1, 2009 93 were the same as above but the final lipid concentration was about 8% (w/w) as opposed to 3% (w/w) in the main trials. Densitometry. Immediately before the densitometric measurements, the samples were degassed by stirring under vacuum for 45 s. This improved the reproducibility significantly but resulted in a small evaporative loss of water (typically 1-5 mg) which was determined by weighing the samples and included in the calculation of the concentrations. The density of lipid suspensions at 40 °C was determined in a vibrating tube densitometer (DMA 602, Anton Parr, Grass, Austria). Technical details regarding loading of samples, calibration, cleaning, statistical treatment, etc., have been reported elsewhere.44 The overall experimental repeatability of the specific volume of lipid suspensions was better than 5 × 10-6 cm3/g. Calorimetry. The phase behavior as a function of composition was deduced from differential scanning calorimetry (DSC) scans (Microcal MC2, Microcal, Amherst, MA). The samples used in the densitometry measurements were diluted 1:20 with Milli-Q water, and the diluted samples were used in DSC measurements. The scans were performed from 10° to 70° at 60 °C/h. Simulations. We used the program NAMD45 with the CHARMM27 all-atom force field and the TIP3 water model46 to conduct molecular dynamics (MD) simulations of a pure, hydrated dimyristoylphosphatidylcholine (DMPC) membrane and DMPC membranes embedded with stearic acid (DMPC/ HSA), stearate (DMPC/NaSA), oleic acid (DMPC/HOA), and oleate (DMPC/NaOA). The DMPC, HSA, and HOA molecules are shown in Figure 5a. We also carried out simulations of pure HOA, HSA, NaOA, and water, but not of pure NaSA, since it is a solid at the temperatures considered here and to our knowledge its crystal structure is not known. The sodium salts are dissociated into a sodium ion and a negatively charged anion, while the protonated acids are undissociated and therefore uncharged. The topology for stearic acid was built by extending palmitic acid (16:0) by two CH2 subunits. Oleic acid was built by modifying the constructed stearic acid. The cis-double bond was placed in the middle of the acyl chain between carbon atoms 9 and 10, where it is found naturally.21,42 Parameters for the cisdouble bond were taken from the CHARMM27 all-atom force field describing the oleoyl cis-double bond in 1-palmytoil-2oleoyl-sn-glycero-3-phosphatidylethanolamine lipid (POPE).46 The initial structure was taken from an equilibrated membrane system consisting of 128 DMPC molecules, and in order to simulate a membrane with fatty acids (FA), a grid of 4 × 4 fatty acid molecules were placed in each monolayer using tcl scripting within the graphical program: Visualization Molecular Dynamics (VMD).47 The total number of fatty acid molecules in each membrane was 32, resulting in a mole fraction of xFA ) 32/(32 + 128) ) 0.20. The fatty acid molecules were aligned with the normal (z-direction) of the membrane and displaced in the z-direction such that the carboxyl group of the fatty acid molecules was placed in the same plane as choline group of DMPC. Each bilayer consisting of 160 molecules (80 in each leaflet; 64 DMPC + 16 FA lipids) was solvated using the program SOLVATE.48 The DMPC and DMPC/FA systems contained ≈4400 and ≈4700 water molecules, respectively. The water layer corresponds to a hydration of ≈34 and ≈37 water molecules per lipid for the DMPC and DMPC/FA bilayers, respectively. In simulations including fatty acid anions, 32 water molecules were chosen randomly and replaced with sodium ions to neutralize the DMPC/FA systems.
94 J. Phys. Chem. B, Vol. 113, No. 1, 2009 All simulations were performed using a time step of 1 fs and were carried out at constant ambient pressure of 1 atm. The pressure was held constant using a Langevin piston method.49 The piston damping coefficient, piston period, and piston decay were set respectively to 5 ps-1, 200 fs, and 500 fs. Anisotropic pressure regulation was applied in the simulations of the membrane systems, while isotropic pressure regulation was used in the bulk water and pure FA simulations. The long-ranged electrostatic forces were calculated using the particle mesh Ewald method.50 The grid spacing was ∼1 Å, and a fourthorder spline was used for the interpolation. Electrostatic forces were updated every fourth femtosecond. Van der Waals interactions were cut off at 12 Å in combination with a switching function starting at 10 Å. Periodic boundary conditions were applied in x-, y-, and z-directions. The potential energy in all systems were initially minimized using 2000 steps of the conjugated gradient method. The lipid membrane systems were simulated for 40-60 ns and the pure compounds for about 10 ns. It was necessary to investigate both the anionic and the protonated form of the fatty acids as the pKa value for the acids increases10,43 upon insertion in a membrane. For example, oleic acid, which has pKa ∼ 5 in aqueous solution, has been shown to have pKa ) 7.6 in an egg phosphatidylcholine membrane,51 and it follows that even small pH changes in the physiological range can shift the degree of protonation considerably. Since the densitometry was done at 313 K, where all DMPC/ OA mixtures and DMPC/SA mixtures (xSA < ∼0.2) are in the fluid phase, it is important for a comparison to the MD simulations that the systems studied by MD simulations also are in the fluid phase. This is, however, not the case when using the original CHARMM27 parameters for phosphatidylcholine lipids.52 We have previously shown that a pure membrane at a temperature above the experimental gel-to-fluid transition temperature has gel phase-like properties as indicated by a too small area per phosphatidylcholine molecule and a too large carbon-deuterium order parameters.52 We found in earlier simulations of a DPPC bilayer membrane that the phase of the membrane system is very sensitive to the charges in the headgroup of the lipids and changed them accordingly by using Mulliken-type charges.53-55 Later developments have shown that we obtained better results for DPPC, when charges derived from the RESP method56 were used. However, this approach has not been verified for DMPC, and we have therefore used the original Mulliken charges and increased the simulation temperature to 330 K to ensure that the pure and mixed bilayers are in the fluid phase as judged by the area of a lipid molecule and NMR order parameters. Only for the pure DMPC are experimental data available. As discussed below in more detail, the area per DMPC molecule and order parameters are in reasonable agreement with experiments.57-59 We found an area of 58 ( 1 Å2/DMPC molecule and an order parameter of ∼0.25 (in the middle of the DMPC fatty acid chain). Both values are within in 5-10% of the experimental data.57-59 The simulations of the bilayer systems, pure HOA, pure NaOA, and water were performed at 330 K. The pure HSA system was simulated at temperatures in the range 330-480 K to determine the temperature where the conformation of the molecules is like the one observed in the membrane, as discussed below. Results and Data Treatment DSC. The DSC experiments were necessary to check the phase behavior of the membrane systems at the temperature
Peters et al.
Figure 1. Transition temperatures (gel-to-fluid phase) for stearic acid and oleic acid as a function of the mole fraction of fatty acid (FA) in DMPC.
used in the densitometry measurements to avoid complications in the interpretation of the results in a coexistence region with two phases of different density. In Figure 1, we have plotted the gel-to-fluid phase transition temperature as a function of the composition of the DMPC/FA system. We see that the influence of the two fatty acids on the transition temperature is qualitatively different; the addition of oleic acid leads to a transition temperature depression, while the addition of stearic acid leads to a transition temperature increase. The transition temperature, which is 23.5 °C for pure DMPC, decreases upon addition of oleic acid at low concentrations about 3 deg and then slowly increases by about 0.5 deg up to a mole fraction of about 0.2. Conversely, a rather large increase in the transition temperature is seen when stearic acid is added. These observations are consistent with previous investigations of the phase behavior of DMPC/FA60 and reflect that the solubility of oleic acid is larger in the fluid phase than in the gel phase (the normal freezing point depression scenario), while the opposite is true for stearic acid. Considering the conformations of the fatty acid molecules, this seems reasonable, considering the conformations of the fatty acid molecules. Thus, the oleic acid molecule with a “kink” at the position of the double bond in the middle of the aliphatic chain is expected to “pack” easier in the fluid membrane with the disordered aliphatic chains of the lipids than in the gel phase with the “straight” ordered lipid acyl chains. For the same reason, it is expected that the stearic acid molecules with their “straight” chains interact more favorably with the gel phase of the lipid bilayer. Densitometry. The specific volume, Vspec, of the tertiary DMPC-FA-water systems was calculated directly from the resonant frequencies measured in the densitometer61 and converted into a molar volume using the molecular weights of DMPC (677.95 g/mol), water (18.02 g/mol), HSA (284.50 g/mol), and HOA (282.50 g/mol). Thermodynamically, the molar volume of the tertiary system may be given in terms of the partial molar volumes according to
Vm ) VH2OxH2O + VDMPCxDMPC + VFAxFA
(1)
where Vi is the partial molar volume of component i at the composition given by the mole fractions xi. If the partial molar volume deviates from its value in the pure state, V /i , the mixture is said to be nonideal, and it is usually associated with some
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special “packing effects” in the mixture. For example, if Vi < V /i , it may be interpreted as if there are interstitial volume or “voids” in the mixture, where the ith component fits, at least partially, so it appears to have a smaller volume in the mixture than in the pure state. Conformational changes of the molecules in the mixture may also lead to a nonideal behavior. The analysis of the volume data for the tertiary mixture is divided into an analysis of two binary mixtures, that is, the (DMPC/FA)-water system and subsequently the DMPC-FA system. The partial molar volume of components A and B in a binary mixture may be determined from the molar volume of the mixture by the standard expressions62
( ) ( ) ∂Vm ∂xB
VA ) Vm - xB
(2)
T,p
∂Vm VB ) Vm + (1 - xB) ∂xB
(3) T,p
We see that only if Vm is a linear function in xB, the partial molar volumes of the two components will be independent of composition and equal to the molar volume in the pure state. Otherwise, they will depend on the composition and there will therefore be a “packing effect”. Application of eqs 2 and 3 requires data for the molar volume Vm of the mixture at a series of mole fractions to enable an accurate determination of the partial derivative at different xB. In many cases, however, these are not available, and instead the so-called apparent molar volumes are determined. They are based on the assumption that the molar volume of a binary mixture may be written as62
Vm ) xAV A/ + xBVB,app
(4)
where it is assumed that the molar volume of one of the components in the mixture (the solvent, A) is the same as in the pure state, such that all nonideality in the mixture is ascribed to the other component (the solute, B). If we know VA/ for the pure component A, VB,app is easily determined from eq 4 and given by
VB,app ) (Vm - xAV A/ )/xB
(5)
The physical significance of the apparent molar volumes is accordingly somewhat obscure, but they are often used as a self-consistent and practical way of analyzing and reporting volumetric data. A simple calculation shows that the relation between the partial molar volume VB and the apparent molar volume VB,app is given by
( )
VB ) VB,app + xAxB
∂VB,app ∂xB
(6) T,p
It is seen that the partial molar and apparent molar volumes are identical when the derivative in eq 6 is equal to zero, and consequently when the apparent molar volume is independent of the composition. This equation also illustrates that VB becomes equal to VB,app in the limits of xB f 0 and xB f 1. To illustrate the calculation of the apparent molar volume of DMPC/FA, we use eq 5, with V A/ ) V /W, the molar volume of pure water at the experimental temperature, and xA ) xw ) 1
Figure 2. Calculated apparent molar volume at 313 K of the DMPC/ FA membranes using eq 5 and plotted as a function of the mole fraction of FA in DMPC. Data for stearic and oleic acid are represented by respectively filled and open symbols. The lines give the molar volume for an ideal mixture. In the inset, the data are plotted in mass-based units (i.e., the specific volume vs the fatty acid weight fraction). The dashed lines are the best second-order polynominal fit, which is used to calculate the partial specific volume in Figure 3B.
- xDMPC/FA, where xDMPC/FA is the mole fraction of the DMPC/ FA pseudo component xDMPC/FA ) (nDMPC + nFA)/(nDMPC + nFA + nW). ni is the number of moles of the ith component. The assumption that V A/ ) V /W as well as the definition of xDMPC/FA implies that all FA is in the membrane. While this is not strictly true since there will be a partitioning between the membrane and the aqueous bulk solution, the partitioning coefficient for a C18 FA is so large63 that the aqueous population will be negligible. The results are shown in Figure 2, where we have plotted the apparent molar volume nonaqVapp of the DMPC/FA mixture as a function of the mole fraction xFA of FA. The drop in the apparent molar volume of the DMPC/HSA system at a mole fraction above ≈0.20 is due to the fact that we have entered the fluid-gel two-phase region at these compositions with the formation of the denser gel phase. But as long as we are in the fluid phase region at mole fractions smaller than ≈0.20, the addition of oleic acid and stearic acid leads apparently to almost the same volumetric effects. Since these are the apparent molar volumes, we cannot in principle conclude anything about a “packing effect” unless it can be argued that the apparent molar volume is identical to the partial volume defined in eqs 2 and 3. To this end, we compare the results in Figure 2 (which were made with a lipid concentration of about 3% (w/w)) with results for ∼8% DMPC/FA samples. For these concentrated suspensions, we observed that FA contents above xFA ∼ 0.18 became too viscous to conduct reproducible densitometric measurements. However, for stearic acid mole fractions of 0.044, 0.085, and 0.160, we obtained reproducible values of nonaqVapp as 655, 639, and 615 cm3/mol, respectively. These results correspond closely to those from the 3% series listed in Figure 2, and we conclude that apparent volume of mixed DMPC-FA does not depend measurably on the lipid concentration. A similar conclusion has previously been made for pure DMPC,31,64 and it follows (eq 6) that the apparent and partial volume functions are indistinguishable. The molar volume of pure aqueous DMPC at 313 K is 667.3 ( 0.6 mL/mol (SEM) (Figure 2), in accordance with previously published values.58,65 The molar volume of pure HSA and pure HOA is respectively 273.166 and 315.4 mL/mol67 at 298.15 K. These values are used to draw the lines DMPC/HOA
96 J. Phys. Chem. B, Vol. 113, No. 1, 2009
Figure 3. (A) The apparent molar volume of fatty acid dissolved in DMPC membranes plotted as a function of the mole fraction of FA in the membranes (xFA). Filled and open symbols refer respectively to stearic acid and oleic acid. The left-hand ordinate gives the apparent specific volume in mL/g as calculated from eq 5. On the right-hand ordinate, the apparent specific volume is given in Å3 per FA molecule. Strictly, this latter axis is valid only for stearic acid (due to the small difference in molecular weight the volumes for oleic acid are marginally (∼0.7%) smaller than the number read off the right ordinate). (B) Partial specific volumes of fatty acids (solid lines) and DMPC (dashed lines) calculated from eqs 2 and 3 and polynominal fits to the data in Figure 2 (the fits are shown as dashed lines in the inset of Figure 2). The error bars are estimated by manually constructing extreme values of the slope in Figure 2.
and DMPC/HSA in Figure 2 representing the molar volume / / xFA + V DMPC xDMPC for an ideal mixture of DMPC Vid ) V FA and FA. For the DMPC/HSA system, we observe a clear positive excess volume of mixing. That is, the partial molar volume of either DMPC or HSA or both are different from the molar volumes of the pure components. The simulations discussed below show that the positive excess volume of mixing is caused by a conformation change of the HSA molecules when embedded in the bilayer membrane. At the experimental temperature 313 K, HSA is a solid (with melting point at 340 K) and has a rodlike shape with all dihedral torsion angles along the chain in their trans-conformation. When embedded in the fluid membrane, the conformation changes from that in the solid to that in the liquid with many gauche defects along the chain, resulting in a larger molar volume. Using the molar volume of liquid HSA (339.06 mL/mol at 353.15K68) as the volume of pure HSA instead of the molar volume of the solid, then the DMPC/stearic acid line for the ideal mixing in Figure 2 moves up to be slightly above the DMPC/oleic acid line for the ideal mixture (line not shown). We see that the experimental points
Peters et al. for the DMPC/HSA mixture all lie close to that line for mole fractions up to about 0.2, where we still are in the one-phase region.60 That is, when corrected for the conformation change of the HSA molecules in the lipid bilayer, the mixture appears nearly to be ideal (Figure 2). While Figure 2 sums up the volumetric behavior of the systems it does not single out subtle deviations from ideality which may be difficult to see because of the large difference in molar volumes of the pure components. This is illustrated in the inset of Figure 2, where we have plotted the same data in specific (rather than molar) units and see small but significant deviations from linearity. To analyze this further, we calculated the apparent specific volume VFA,app of the fatty acids and the partial specific volume of both fatty acid and DMPC (VFA and VDMPC). For the apparent volumes, we use a version of eq 5, in which VB,app ) VFA,app, Vm ) nonaqVapp, / V A/ ) V DMPC , and xA ) xDMPC ) 1 - xFA, with xFA ) nFA/ / (nFA + nDMPC). V DMPC is the experimental specific volume of pure DMPC (0.9843 mL/g) derived from eq 1 at xFA ) 0. Thus, VFA,app is the apparent volume taken up by the fatty acid in the membrane assuming that the volume of DMPC remains unchanged by the solute, and this parameter is directly comparable with the volumes derived from the simulations (see below). It appears from Figure 3A that the apparent specific volume at the lowest mole fractions xFA is about 1.2 and 1.3 mL/g for respectively oleic acid and stearic acid. The volumes decrease as xFA becomes larger, and both fatty acids have apparent specific volumes of about 1.1 mL/g (corresponding to ∼520 Å3 per FA molecule) at xFA ≈ 0.2. For comparison, pure liquid oleic acid has a specific volume of 1.12 mL/g at 298.15 K.67 We have also determined the partial specific volumes VFA and VDMPC using eqs 2 and 3 on the data in the inset of Figure 2 and plotted the results in Figure 3B.69,70 The slopes on the right-hand side of eqs 2 and 3 were derived from polynomial fits to data for each fatty acid in Figure 2 (dashed lines in the inset of the figure). For stearic acid, we only used data well below the assumed phase boundary at xSA ∼ 0.2. The VFA functions generally follow the picture seen for the apparent volumes, except for rather low values of VSA at the higher SA concentrations. This may reflect packing as the system is brought closer to the transition into the much denser gel phase. Figure 3B also illustrates the partial specific volume of DMPC in the mixture, and it appears that even at the highest xFA values, VDMPC remains practically unchanged and equal to the volume of the pure lipid. This observation parallels recent studies of cholesterol in PC membranes70 and suggests that at PC:FA molar ratios of 5-10 the volume of the “solvent” PC molecules is only marginally perturbed by FA. We conclude that at low concentrations, the fatty acids mix with DMPC with a slight increase in volume (VFA is 10-15% larger than the volume of the pure liquid fatty acid). At higher concentrations (xFA > 0.1), this effect vanishes, and the mixture of DMPC and FA appears to be ideal. Simulations: Volumetric Data. We first report volumetric data extracted from the simulations, since they can be compared directly with the experimental volumetric data and used to validate the simulations. The volume of the simulation box. V, were determined for all systems on the basis of 250 ps block averages over a 20-40 ns period subsequent to the equilibration. The standard deviation on V, estimated from the scatter and standard procedures for error propagation, ranged from 0.1 to 0.4%. The simulated values of Vm, V /DMPC, and V w/ at the composition xFA ) 0.20 were inserted in eq 5
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TABLE 1: Volumetric Data from the Simulations at 330 Ka nonaq
V
Vapp
3
system pure water pure HSA at 385 K pure HSA at 330 K pure HOA pure NaOA DMPC DMPC-HSA-water DMPC-HOA-water DMPC-NaSA-water DMPC-NaOA-water
VFA,app
Å/ Å/ Å3/ cm3/g molecule cm3/g molecule cm3/g molecule 0.988 1.186 0.921 1.164 1.081 0.969 0.978 0.981 0.973 0.975
296 560 435 546 546 n/a n/a n/a n/a n/a
3
n/a n/a n/a n/a n/a 0.953 0.965 0.972 0.959 0.963
n/a n/a n/a n/a n/a 1073 n/a n/a n/a n/a
n/a n/a n/a n/a n/a n/a 1.084 1.153 1.014 1.051
n/a n/a n/a n/a n/a n/a 512 541 531 516
a The volume, V, was derived directly from the dimensions of the simulation box and inserted in eq 5 to calculate respectively the apparent volume of the mixed membrane, nonaqVapp, and the apparent volume of the fatty acid in the membrane, VFA,app. The mole fraction of FA in the DMPC membrane is 0.2. For pure HSA, entries at two temperatures are given. At the simulation temperature, 330 K, it is a solid, while at 385 K it is a liquid with molecular conformations like found for the embedded molecules in DMPC at 330 K.
to calculate the apparent volume of the nonaqueous phase, nonaq Vapp, and the apparent volume of the fatty acid in the membrane, VFA,app, like for the experimental data. This procedure inevitably increases the standard deviation which was about 0.5% for the first and 5% for the latter of these parameters. Values of the three volumetric functions are listed in Table 1, where the volume of HSA is given at two temperatures, because pure HSA is crystalline at 330 K and because the conformation of the molecules in the membrane was found to be very different from that in the crystalline phase. That raised the question, which pure HSA volume should be used in a comparison with the volume of the molecules in the membrane: the volume of a molecule in the crystalline state or in a state with the same molecular conformation? We found that the molecular conformation of HSA in the membrane is the same as the one found in pure HSA at 385 Ksjust at the melting temperature of HSA found from simulation, as will be discussed later. From Figure 2, we find the experimental volume nonaqVapp ) 596 cm3/mol corresponding to 0.995 cm3/g for both DMPC-FA systems at xFA ) 0.2. These values compare well with the simulation results (to within 3%; Table 1) as does the (more sensitive) experimental value for VFA,app ) 1.10 cm3/g (to within 2%; Figure 3 and Table 1). This seems to validate the simulations, and we will in the following describe structural details about the systems that could not be determined experimentally. Simulations: Lateral Area and Thickness. We have monitored the area/lipid molecule as a function of time for two reasons. One is to check that the membrane is in the fluid phase, which may be inferred from the area per lipid, and the other is to make sure that the system is equilibrated, which may be judged from the time evolution of the area. At equilibrium, it should fluctuate around a steady time-independent value. The results are shown in Figure 4. The system is started in a nonequilibrated state, and we see in both cases an initial drop in the area followed by a leveling off around a constant value. The area per DMPC molecule was 58 ( 1 Å2 for pure DMPC (data not shown), and this value compares reasonable well with experimental results (within 2-5%) of 59.6 and 60.6 ( 0.5 Å2/ molecule reported respectively by Petrache et al.58 and Kucerka et al.59 For the mixed membranes, the average surface areas per DMPC molecule were 63.2 ( 1.1 Å2 (DMPC/HOA), 67.9 ( 1.3 Å2 (DMPC/NaOA), 59.8 ( 1.2 Å2 (DMPC/HSA), and
Figure 4. Time course of the area per DMPC molecule for membranes doped with (a) stearic or (b) oleic acid in respectively the protonated (neutral, HFA) and anionic (charged, NaFA) states.
65.3 ( 0.8 Å2 (DMPC/NaSA). These results show that deprotonation leads to an expansion of the lateral area and that the expansion is larger when oleic acid is introduced, probably because of the “kink” at the double bond. This may be illustrated more clearly by the apparent surface area of FA, AFA,app. This parameter is a two-dimensional analogue to the apparent volume (eq 5) and defined as the total surface increase resulting from FA insertion devided by the number of inserted acid molecules. For SA (OA), AFA,app is respectively 7 Å2 (17 Å2) and 29 Å2 (40 Å2) for the protonated and anionic forms. The structural perturbations introduced by the fatty acids were further investigated by an analysis of the average position of selected atoms in both DMPC and FA relative to the center of mass coordinate of the combined DMPC/FA system in the z-direction perpendicular to the plane of the membrane (C.O.M.membrane). Figure 5 provides an overview of the results, and it appears that the fatty acids bring about some characteristic changes in the structure depending strongly on the protonation status of the acid. Thus, the carboxyl carbon atom C1 (see the location of C1 in Figure 5a) of the neutral (protonated) acids had average positions ∼13-14 Å from C.O.M.membrane (Figure 5b). This corresponds to about two carbon segments below the carboxyl group of the DMPC chains, a position which is essentially dehydrated. Conversely, the acid anions have their carboxyl carbon atoms (C1) at around 15-16 Å from C.O.M.membrane, which is a partially hydrated position at the outer part of the glycerol backbone. That is, there seems to be a tendency for the protonated FA to move deeper into the
98 J. Phys. Chem. B, Vol. 113, No. 1, 2009
Peters et al.
Figure 6. Probability distribution of the location of methyl groups from DMPC and oleic acid along the membrane normal: (top) DMPC/ HOA; (bottom) DMPC/NaOA. The center of mass of the DMPC/FA system is located at z ) 0.
Figure 5. (a) Sketches of the HSA, HOA, and DMPC molecules with an identification of the atom numbers used in (b). In HOA, the double bond is located at atom C9, giving rise to a “kink” in the aliphatic chain. For clarity, no hydrogen atoms are shown. (b) Position of selected atoms along the membrane normal relative to the center of mass of the membrane system. For each of the five systems, the solid and open symbols represent respectively atoms in the DMPC and fatty acid molecules. The letters given identify the selected atoms and their location in the lipid/FA structures defined in (a). The error bars represent the fluctuations in the system. The dashed lines included as a guidance correspond to the average positions of C25, O32, and O11 for pure DMPC.
membrane. When we look at selected atom positions in the DMPC molecules (N, P, O11, O32, and C25) with the average positions C25, O32, and O11 for pure DMPC (shown as dashed lines in Figure 5b), there seems to be a small tendency for the lipid molecules to “stretch” out with the protonated forms as compared to the pure membrane and the membrane with the acid anions. This increase of the thickness of the membrane combined with a drop in the area (Figure 4) tends to preserve the volume of the membrane, a feature often seen in membrane physics and corroborated by the current densitometric measurements. The coupling between thinning and lateral expansion when the protonated form of the FA is replaced by the anionic form may also cause an increased interdigitation of the acyl chains in the membrane core. To assess this, we determined the probability distribution of the methyl groups at the end of the aliphatic chains belonging to each leaflet. Results for DMPC and oleic acid (HOA and NaOA) shown in Figure 6 reveal that the distribution of lipid -CH3 is shifted slightly inwards and broadened when the proton is removed from the fatty acid. This change, which was also observed for DMPC/HSA and DMPC/ NaSA systems (data not shown), suggests an increased degree of lipid chain interdigitation, and we conclude that the thinning
induced by fatty acid anions relies on an increase in both chain disorder and interdigitation. Figure 6 also shows that the average position of the fatty acid methyl group appears to be unaffected by its protonation status, while the distribution is a little broader with the FA anions, implying an increase in the interdigitation of the FAs in the two leaflets. Simulations: Structure along the Membrane Normal. Structural effects on FA and DMPC are further illustrated by the acyl chain order parameters deduced from the carbondeuterium order parameter (SCD) calculated as
SCD ) |〈3/2(cos2 θ) - 1/2〉|
(7)
where θ is the angle between the carbon-deuterium bond and the membrane normal.71 〈...〉 implies an average over time and molecules. The first 20 ns of each simulation was taken as an equilibration phase and discarded from the calculations. Results for the DMPC chains (with or without fatty acid) and the fatty acid chains are shown in Figure 7. The data for the pure DMPC membrane (filled triangles in Figure 7a) are in accord with experimental results for fluid membranes.53,56 The protonated form of the fatty acids induces more order in the DMPC acyl chains than the corresponding anions. This is consistent with the “stretch” of the DMPC acyl chain concluded from Figure 5 and the reduction in the lateral area seen in Figure 4. Furthermore, the saturated acid and salt (HSA and NaSA) induce more order in the DMPC chains than their unsaturated counterparts (HOA and NaOA). The effects, however, are moderate, and the bilayers remain in the fluid state. The order parameters of the fatty acid chains (Figure 7b) show large differences between stearic and oleic acid around the ninth carbon atom (Figure 5a), where oleic acid has its double bond and exhibits much less order than the saturated fatty acid. Comparisons of the corresponding acid/base pairs show that the anionic form is the more ordered, particularly so at the highest carbon numbers (towards the core of the membrane). This is consistent with the results in Figures 5 and 6b, where we found that FAs were more “stretched” out when in the anionic form. Simulations: Aliphatic Chain Conformations in FA. Another measure of the conformation of the fatty acids in the
Molecular Packing of Fatty Acids in Bilayers
J. Phys. Chem. B, Vol. 113, No. 1, 2009 99
Figure 9. Probability distribution of the end-to-end distances for (a) HSA embedded in the DMPC membrane at xFA ) 0.2 and (b) NaSA embedded in the DMPC membrane at xFA ) 0.2.
Figure 7. Order parameters, |SCD|, for (a) the aliphatic chains DMPC and (b) fatty acids. The different systems are identified in the inset.
Figure 8. Probability distribution of the end-to-end distance for HOA and NaOA in the pure bulk phase (top) and embedded in DMPC at a mole fraction of 0.2 (bottom).
membrane is the end-to-end distance, which on the average becomes smaller with increasing temperature as a result of the introduction of more and more gauche defects in the aliphatic chain.72-76 At low temperature all dihedral angles will be in the trans conformation, resulting in an end-to-end distance of about 20 Å for HOA. In Figure 8, distributions over the endto-end distance in HOA and NaOA are shown for both the pure bulk form and in the membrane at 330 K. In the bulk, the distributions for oleic acid are very similar for both the protonated form and the Na salt with a relative broad distribution around a peak at ≈16 Å and a long tail down to a few
Figure 10. Probability distribution of the end-to-end distance for HSA in the pure bulk phase at (a) 300, (b) 380, and (c) 390 K. (d) Probability distribution of end-to-end distance for HSA when embedded in the DMPC membrane at a mole fraction of 0.2 at 330 K.
angstroms. Considering the distributions for the two forms of the fatty acid in the membrane, we see that there is a difference. It is clear that the aliphatic chain in the Na salt of the fatty acid is more stretched out than in the protonated form consistent with the conclusion that the charged carboxyl group is closer to the DMPC headgroup than the uncharged carboxyl group. A similar effect is seen for stearic acid as shown in Figure 9. In contrast to what was found for HOA, there is a significant change in the conformation of pure HSA, when introduced in the membrane. With all dihedral angles in the trans conformation, the end-to-end distance is 21.19 Å, and from Figure 10d (or Figure 9), we see a rather broad distribution of the end-to-end distance with a peak around 18 Å and a tail extending down to about 10 Å for HSA in the membrane at 330 K. The end-to-end distance for HSA at 330 K in the membrane (Figure 10d) is rather similar to that of HOA in Figure 8 with the exception that the tail in the distribution function for HSA does not extend down to as small values as for the HOA system. This implies that, unlike for HOA, there is no sign of a population of HSA molecules in DMPC which are bent in the sense that the carbonyl and methyl groups are close. However, the distribution of HSA in DMPC is much broader than the distribution of bulk HSA (Figure 10a-b) in the 300-380 K temperature range. The reason is that pure HSA is crystalline both experimentally and in the simulations at 330 K. We have therefore done simulations of pure HSA starting with the low-temperature experimental monoclinic crystalline structure with space group P21/a66 to find a temperature where the end-to-end distribution in pure HSA is the same as found for embedded HSA (Figure 10d). In the crystal structure, the molecules are arranged in lamellas consisting of pairs of molecules with
100 J. Phys. Chem. B, Vol. 113, No. 1, 2009
Figure 11. Volume per molecule of pure HSA as a function of temperature. Snapshots display representative conformations at T ) 300, 380, and 440 K.
the carboxyl groups pointing toward each other, enabling them to form two hydrogen bonds for each carboxyl group, which stabilizes the structure. We monitored the end-to-end distance (Figure 10) and volume (Figure 11) as a function of temperature in a series of simulations at a constant pressure of 1 atm and determined the melting transition temperature. The melting temperature was identified as the temperature, where there was an inflection point in the volume vs temperature curve. It appears from Figure 11 that HSA melted at ≈385 K, which is 42 K above the experimental melting temperature. This is like the gel-to-fluid transition temperature for the DMPC membrane that also was higher in the simulations than in the experiments and it is due to artifacts in the potentials used in the simulations and possibly the lack of imperfections in the crystal structure and free surfaces. The identification of the temperature at the inflection point as the melting temperature was confirmed by a determination of the end-to-end distance as seen from the plots in Figure 10. Up to 380 K, the end-to-end distance distribution is narrow, which means that only few gauche defects have been introduced, but at 390 K the distribution is much wider because many gauche defects have been introduced, causing the translational order to be lost and a fluid phase is formed. The end-to-end distance distribution at 390 K is almost like the one found when the acid is embedded in the membrane at 330 K. No attempt has been made to find the temperature where the match between the end-to-end distance distributions is optimal. Since the distribution at 390 K is slightly broader than the distribution for the embedded molecules, it is suggested to use the volume at the melting point, 385 K, as the volume of the pure HSA rather than the volume of the solid at 330 K, when the excess volumes in mixtures with HSA is calculated. In that way, we eliminate the influence of the conformation change on the results and allow us to evaluate if there are any “packing effects” in the mixture, as discussed previously. A similar analysis has not been made for pure NaSA, since to our knowledge its crystalline structure is not known and there are no experimental results to compare with. Discussion The MD data reveal a number of general trends for the changes in membrane structure brought about by fatty acids and emphasize that these changes are highly dependent on the
Peters et al. protonation status of the acid. Although both forms interchelate between the lipid chains, with an overall direction parallel to the membrane normal, the protonated molecules (HSA and HOA) position themselves rather deeply in the membrane where the -COOH group is mainly dehydrated (Figure 5). This leads to a comparably low degree of order in the fatty acid chain (Figure 7b) and a concomitant “stretching” (Figure 5) or ordering (Figure 7a) of the adjacent DMPC acyl chains. As a result, the DMPC bilayer becomes 2-3 Å thicker upon the addition of HSA and HOA (Figure 5). In the lateral plane, the protonated acids only produce a limited expansion. Thus, the apparent lateral areas, AFA,app, were respectively 7 and 17 Å2 for HSA and HOA. In comparison, the lateral area in a fatty acid monolayer is about 21 Å2 at the tilt transition.77 The low AFA,app values for membrane lodged (protonated) fatty acids suggest that they are capable of utilizing free or “interstitial” space and hence produce an expansion which is smaller than their intrinsic lateral area. Comparably low AFA,app values have previously been reported for a number of alcohols-PC systems,54,78,79 and it appears that tighter lateral packing is a typical property of membranes doped with a noncharged amphiphile. The results for the fatty acid anions are quite different. The most conspicuous change resulting from deprotonation is the movement of the COO- group towards the membrane interface (Figure 5). This stretching of the fatty acid anion obviously increases its order parameter (Figure 7b). Interestingly, however, the order parameter of the lipid chains decreases when the acids lose the proton (Figure 7a). The latter behavior most likely relies on the electrostatic repulsion between the acid anions, which tends to laterally expand the bilayers. This is clearly illustrated in the AFA,app function, which is 2-3 times higher (30-40 Å2) for the anionic acids, and we suggest that it is this more open lateral arrangement, which allows the lipid chains to attain a higher average number of gauche conformations (and hence a thinner and more disordered membrane). The distinctive lateral and normal changes in membrane structure discussed above tend to compensate such that the membrane volume only changes moderately. Thus, the simulated values of VFA,app (Table 1) were rather similar for all FA species (510-540 Å3/molecule) with no systematic dependence on the protonation status. The simulations compare well with the experimental value at the same xFA (∼530 Å3/molecule for both fatty acids). The degree of protonation underlying the latter (experimental) result is unknown, but measurements in the (unbuffered) samples from the densitometry showed pH 6.4-6.8, and as pKa for membrane lodged fatty acids is reported to lie in the 6.5-8.0 range,51,80-82 the densitometric results represent a distribution of fatty acids and their corresponding basesmost likely with a dominance of the former species. At xFA ) 0.05, the apparent volume of stearic acid was 594 ( 6 Å3 (SEM). This is well over the value for liquid SA at the melting point (∼540 Å3/molecule), but a more interesting comparison may arise from the use of so-called component volumes for fatty acid chains in fully hydrated PC bilayers.83-85 Using these additivity schemes and an estimated value of 32 Å3 for the volume of a -COOH group,86 we find volumes of about 515-530 Å3 for the two fatty acids. These values represent the expected volume of the free fatty acids if it had the same properties as the acyl chains in the pure PC bilayer. We conclude that at intermediate concentrations (xFA > 0.1) the inserted fatty acids have overall volumes properties similar to the ester-bonded fatty acid in a PC membrane, while at the lower concentrations, PC-FA interactions generate a slight positive excess volume.
Molecular Packing of Fatty Acids in Bilayers Conclusion We have applied molecular dynamics simulations and experimental density measurements (densitometry) to study the molecular packing and structure of an unsaturated fatty acid (oleic acid) and a saturated fatty acid (stearic acid) in fluid bilayers of dimyristoylphosphatidylcholine. The experimentally determined densities reveal that at low fatty acid concentrations the fatty acids mix with DMPC with a slight increase in the partial specific volume, which is 10-15% larger than the volume of the pure liquid fatty acid. At higher concentrations (xFA > 0.1), this effect vanishes, and DMPC and FA form an ideal mixture. The simulation results agree well with the densitometric data, and additional revealed interesting differences in the structure and location of the fatty acids depending on the protonation status of the fatty acid. The carboxyl group of the protonated (neutral) acids had average positions that correspond to about two carbon segments below the carboxyl group of the DMPC chainssa position which is essentially dehydrated. In contrast, the carboxyl group of the deprotonated (charged) acids is on the average located at the outer part of the glycerol backbone, which is a partially hydrated position. Furthermore, the protonated form of the fatty acids induces more order in the DMPC acyl chains than the corresponding anions. This is consistent with the observed “stretch” of the DMPC acyl chain and the reduction in the lateral area. Hence, the opposing effects of protonation and deprotonation on the lateral and normal dimensions of the membrane tend to cancel so that the density depends only weakly on this parameter. Membrane order and thickness, however, appear to respond rather strongly to protonation of free fatty acids, and this may be of biological importance as membrane bound fatty acids with pKa close to 751 will be prone to significant shifts in the degree of protonation within a physiologically relevant range of pH. Acknowledgment. G.H.P. and P.W. acknowledge financial support from the Danish National Research Foundation via a grant to the MEMPHYS-Center for Biomembrane Physics. Simulations were performed at the Danish Center for Scientific Computing at the University of Southern Denmark. References and Notes (1) Singer, S. J.; Nicolson, G. L. Science 1972, 175, 720–731. (2) Israelachvili, J. N.; Marcelja, S.; Horn, R. G. Q. ReV. Biophys. 1980, 13, 121–200. (3) Dowhan, W. Annu. ReV. Biochem. 1997, 66, 199–232. (4) Hampton, M. J.; Floyd, R. A.; Clark, J. B.; Lancaster, J. H. Chem. Phys. Lipids 1980, 27, 177–183. (5) Gudi, S.; Nolan, J. P.; Frangos, J. A. Proc. Natl. Acad. Sci. U.S.A. 1998, 95, 2515–2519. (6) Mouritsen, O. G.; Andresen, T. L.; Halperin, A.; Hansen, P. L.; Jakobsen, A. F.; Jensen, U. B.; Jensen, M. Ø.; Jørgensen, K.; Kaasgaard, T.; Leidy, C.; Simonsen, A. C.; Peters, G. H.; Weiss, M. J. Phys.: Condens. Matter 2006, 18, 1–12. (7) Leidy, C.; Linderoth, L.; Andresen, T. L.; Mouritsen, O. G.; Jørgensen, K.; Peters, G. H. Biophys. J. 2006, 90, 3165–3175. (8) Ohlrogge, J.; Browse, J. Plant Cell 1995, 7, 957–970. (9) Millar, A. A.; Wrischer, M.; Kunst, L. Plant Cell 1998, 11, 1889– 1902. (10) Peters, G. H.; Dahmen-Levison, U.; de Meijere, K.; Brezesinski, G.; Toxvaerd, S.; Svendsen, A.; Kinnunen, P. K. J. Langmuir 2000, 16, 2779–2788. (11) Porat, N.; Gill, D.; Parola, A. H. J. Biol. Chem. 1988, 263, 14608– 14611. (12) Cybulski, L. E.; Albanesi, D.; Mansilla, M. C.; Altabe, S.; Aguilar, P. S.; De Mendoza, D. Mol. Microbiol. 2002, 45, 1379–1388. (13) Vigh, L.; Maresca, B.; Harwood, J. L. Trends Biochem. Sci. 1998, 23, 369–374. (14) Razzao, T. M.; Ozegbe, P.; Jury, E. C.; Sembi, P.; Blackwell, N. M.; Kabouridis, P. S. Immunology 2004, 113, 413–426.
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