Lipid Diffusion, Free Area, and Molecular Dynamics Simulations
2005; Elsevier BV; Volume: 88; Issue: 6 Linguagem: Inglês
10.1529/biophysj.105.059766
ISSN1542-0086
AutoresPaulo F. Almeida, Winchil L.C. Vaz, T. E. Thompson,
Tópico(s)Protein Structure and Dynamics
ResumoIn a recent article in Biophysical Journal, Falck et al., 2004Falck E. Patra M. Karttunen M. Hyvönen M.T. Vattulainen I. Lessons of slicing membranes: interplay of packing, free area, and lateral diffusion in phospholipid/cholesterol bilayers.Biophys. J. 2004; 87: 1076-1091Abstract Full Text Full Text PDF PubMed Scopus (239) Google Scholar present a molecular dynamics (MD) study of phosphatidylcholine (PC)/cholesterol (Chol) bilayers, focusing on the lipid packing and its relation to free area and lateral diffusion of lipids. A significant comparison is made between their MD results and our experimental diffusion measurements using fluorescence recovery after photobleaching (FRAP) and the analysis of those experiments using the free area model (Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google Scholar). In contrast to our conclusion, Falck et al. state that the free area model does not quantitatively represent lipid diffusion. Furthermore, their simulations predict a much stronger effect of cholesterol on diffusion than found experimentally. In our opinion, as written, some of the statements of Falck et al. are prone to misinterpretation. The criticism of the free are model based on the MD simulations is flawed because comparison is made between different systems. If the proper systems are compared, the free area model actually predicts the correct result for lipid diffusion, whereas the MD simulations do not. In this Comment to the Editor, we present our views on the problem and clarify several of the issues. Finally, we attempt to resolve the apparent quantitative disagreement between the MD simulations and our experiments on lipid diffusion. A brief summary of experimental diffusion measurements and the phase diagram of phospholipid/cholesterol mixtures is useful to follow this discussion. Above the main phase transition temperature (Tm) of the phospholipid, its mixtures with cholesterol result in a phase diagram with three different regions: if the mol fraction of Chol (χcho) is <∼0.1 (depending on temperature), the system is in an liquid-disordered (ℓd) phase; above χcho ≈ 0.30, the system is in a liquid-ordered (ℓo) phase (which may also be called a phospholipid/cholesterol condensed complex region; McConnell and Radhakrishnan, 2003McConnell H.M. Radhakrishnan A. Condensed complexes of cholesterol and phospholipids.Biochim. Biophys. Acta. 2003; 1610: 159-173Crossref PubMed Scopus (357) Google Scholar); and, in between those Chol concentrations, ℓd and ℓo phases coexist (Shimshick and McConnell, 1973Shimshick E.J. McConnell H.M. Lateral phase separations in binary mixtures of cholesterol and phospholipids.Biochem. Biophys. Res. Commun. 1973; 53: 446-451Crossref PubMed Scopus (208) Google Scholar; Ipsen et al., 1987Ipsen J.H. Karlström G. Mouritsen O.G. Wennerstrom H. Zuckermann M.J. Phase equilibria in the phosphatidylcholine-cholesterol system.Biochim. Biophys. Acta. 1987; 905: 162-172Crossref PubMed Scopus (902) Google Scholar; Sankaram and Thompson, 1990bSankaram M.B. Thompson T.E. Interaction of cholesterol with various glycerophospholipids and sphingomyelin.Biochemistry. 1990; 29: 10670-10675Crossref PubMed Scopus (293) Google Scholar; Vist and Davis, 1990Vist M.R. Davis J.H. Phase equilibria of cholesterol/dipalmitoylphosphatidylcholine mixtures: 2H-nuclear magnetic resonance and differential scanning calorimetry.Biochemistry. 1990; 29: 451-464Crossref PubMed Scopus (1014) Google Scholar; Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google Scholar). In our work (Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google Scholar), the lateral diffusion coefficient of the phospholipid (DL) in dimyristoylphosphatidylcholine (DMPC)/Chol mixtures drops by a factor of 2.2 from the ℓd phase DMPC, in the absence of cholesterol (Vaz et al., 1985Vaz W.L.C. Clegg R.M. Hallmann D. Translational diffusion of lipids in liquid-crystalline phase phosphatidylcholine multibilayers: a comparison of experiment with theory.Biochemistry. 1985; 24: 781-786Crossref PubMed Scopus (273) Google Scholar), to the ℓo phase with at least χcho = 0.30 (Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google Scholar). This is in agreement with measurements by different investigators, over two and half decades, using different techniques, as shown in Table 1, which emphasizes DMPC/Chol because this is the system we examined. For the phospholipid/cholesterol systems listed here, the ratio of DL in ℓd-phase phospholipid to DL in ℓo-phase phospholipid/cholesterol is always between 2 and 4, with an average value of 2.7 ± 0.7. Korlach et al., 1999Korlach J. Schwille P. Webb W.W. Feigenson G.W. Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy.Proc. Natl. Acad. Sci. USA. 1999; 96: 8461-8466Crossref PubMed Scopus (720) Google Scholar also report a measurement at χcho = 0.60 in dilauroylphosphatidylcholine (DLPC)/Chol. This measurement differs from the data reported by other investigators on other PC/Chol systems in that it is the only one that shows a significant decrease in DL in the ℓo phase, upon increase in the cholesterol content beyond χcho = 0.30.Table 1Comparison of diffusion coefficients in the ℓd and ℓo phases for a few phospholipid/cholesterol systemsSystemXchoT (°C)PhaseD (cm2s−1)RatioMethodReferenceDMPC035ℓd7.5 × 10−8–FRAPRubenstein et al., 1979Rubenstein J.L.R. Smith B.A. McConnell H.M. Lateral diffusion in binary mixtures of cholesterol and phosphatidylcholines.Proc. Natl. Acad. Sci. USA. 1979; 76: 15-18Crossref PubMed Scopus (276) Google ScholarDMPC/Chol≥0.3035ℓo3.0 × 10−82.5––DMPC026ℓd6.0 × 10−8–FRAPAlecio et al., 1982Alecio M.R. Golan D.E. Veatch W.R. Rando R.R. Use of a fluorescent cholesterol derivative to measure the lateral mobility of cholesterol in membranes.Proc. Natl. Acad. Sci. USA. 1982; 79: 5171-5174Crossref PubMed Scopus (76) Google ScholarDMPC/Chol≥0.3026ℓo1.8 × 10−83.3––DMPC035ℓd7.6 × 10−8–FRAPVaz et al., 1985Vaz W.L.C. Clegg R.M. Hallmann D. Translational diffusion of lipids in liquid-crystalline phase phosphatidylcholine multibilayers: a comparison of experiment with theory.Biochemistry. 1985; 24: 781-786Crossref PubMed Scopus (273) Google ScholarDMPC/Chol≥0.3034ℓo3.5 × 10−82.2–Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google ScholarDLPC025ℓd3 × 10−8–FCSKorlach et al., 1999Korlach J. Schwille P. Webb W.W. Feigenson G.W. Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy.Proc. Natl. Acad. Sci. USA. 1999; 96: 8461-8466Crossref PubMed Scopus (720) Google ScholarDLPC/Chol0.3025ℓo1 × 10−83––DMPC035ℓd11 × 10−8–pfg-NMRFilippov et al., 2003Filippov A. Orädd G. Lindblom G. The effect of cholesterol on the lateral diffusion of phospholipids in oriented bilayers.Biophys. J. 2003; 84: 3079-3086Abstract Full Text Full Text PDF PubMed Scopus (354) Google ScholarDMPC/Chol0.3335ℓo3 × 10−84––SM055ℓd8 × 10−8–pfg-NMRFilippov et al., 2003Filippov A. Orädd G. Lindblom G. The effect of cholesterol on the lateral diffusion of phospholipids in oriented bilayers.Biophys. J. 2003; 84: 3079-3086Abstract Full Text Full Text PDF PubMed Scopus (354) Google ScholarSM/Chol0.30–0.42555ℓo3.5 × 10−82.3––DOPC030ℓd10 × 10−8–pfg-NMRFilippov et al., 2003Filippov A. Orädd G. Lindblom G. The effect of cholesterol on the lateral diffusion of phospholipids in oriented bilayers.Biophys. J. 2003; 84: 3079-3086Abstract Full Text Full Text PDF PubMed Scopus (354) Google ScholarDOPC/Chol0.3330ℓo(?)5 × 10−82–– Open table in a new tab In our measurements, DL does not decrease with Chol content in the ℓd phase; a significant decrease is only observed when the χcho is high enough for the system to enter the ℓd–ℓo coexistence region (Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google Scholar). That lack of dependence of DL on χcho in the ℓd phase is also apparent in the data from McConnell's group (Rubenstein et al., 1979Rubenstein J.L.R. Smith B.A. McConnell H.M. Lateral diffusion in binary mixtures of cholesterol and phosphatidylcholines.Proc. Natl. Acad. Sci. USA. 1979; 76: 15-18Crossref PubMed Scopus (276) Google Scholar) for DMPC/Chol and egg PC/Chol, and in the data of Filippov et al., 2003Filippov A. Orädd G. Lindblom G. The effect of cholesterol on the lateral diffusion of phospholipids in oriented bilayers.Biophys. J. 2003; 84: 3079-3086Abstract Full Text Full Text PDF PubMed Scopus (354) Google Scholar for chicken egg sphingomyelin (SM)/Chol. The onset of the decrease of DL with χcho agrees well with the two-phase boundary of the phase diagram for DMPC/Chol (Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google Scholar) and SM/Chol (Filippov et al., 2003Filippov A. Orädd G. Lindblom G. The effect of cholesterol on the lateral diffusion of phospholipids in oriented bilayers.Biophys. J. 2003; 84: 3079-3086Abstract Full Text Full Text PDF PubMed Scopus (354) Google Scholar). Data of Filippov et al., 2003Filippov A. Orädd G. Lindblom G. The effect of cholesterol on the lateral diffusion of phospholipids in oriented bilayers.Biophys. J. 2003; 84: 3079-3086Abstract Full Text Full Text PDF PubMed Scopus (354) Google Scholar on DMPC/Chol and dioleoylphosphatidylcholine (DOPC)/Chol, on the other hand, show a monotonic decrease of DL with Chol concentration even in the ℓd phase. These data of Filippov et al., 2003Filippov A. Orädd G. Lindblom G. The effect of cholesterol on the lateral diffusion of phospholipids in oriented bilayers.Biophys. J. 2003; 84: 3079-3086Abstract Full Text Full Text PDF PubMed Scopus (354) Google Scholar appear to be also in conflict with earlier measurements by the same group in DOPC/Chol (Lindblom et al., 1981Lindblom G. Johansson L.B.A. Arvidson G. Effect of cholesterol in membranes. Pulsed nuclear magnetic resonance measurements of lipid lateral diffusion.Biochemistry. 1981; 20: 2204-2207Crossref PubMed Scopus (94) Google Scholar). Filippov et al., 2003Filippov A. Orädd G. Lindblom G. The effect of cholesterol on the lateral diffusion of phospholipids in oriented bilayers.Biophys. J. 2003; 84: 3079-3086Abstract Full Text Full Text PDF PubMed Scopus (354) Google Scholar discuss these apparent discrepancies. Falck et al., 2004Falck E. Patra M. Karttunen M. Hyvönen M.T. Vattulainen I. Lessons of slicing membranes: interplay of packing, free area, and lateral diffusion in phospholipid/cholesterol bilayers.Biophys. J. 2004; 87: 1076-1091Abstract Full Text Full Text PDF PubMed Scopus (239) Google Scholar conclude their introduction by stating that free area theories correctly predict a reduction in diffusion caused by the addition of cholesterol to a PC membrane, "but are not applicable to quantitatively describing lateral diffusion in lipid bilayers." Without qualification, this statement appears to apply both to MD simulations and experimental data. Further, in their discussion they add: "In our opinion, one should at least not expect free area theory to yield quantitative results." These statements are contrary to our conclusions. First, Vaz et al., 1985Vaz W.L.C. Clegg R.M. Hallmann D. Translational diffusion of lipids in liquid-crystalline phase phosphatidylcholine multibilayers: a comparison of experiment with theory.Biochemistry. 1985; 24: 781-786Crossref PubMed Scopus (273) Google Scholar showed that the free area model can indeed fit the experimental diffusion data quantitatively, when a change in free volume is caused by a change in temperature. Second, Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google Scholar, extended this study to the effect of cholesterol, as an obvious way of changing the free volume, using a version of the Macedo-Litovitz equation (Eq. 1) (Macedo and Litovitz, 1965Macedo P.B. Litovitz T.A. On the relative roles of free volume and activation energy in the viscosity of liquids.J. Chem. Phys. 1965; 42: 245-256Crossref Scopus (445) Google Scholar) for the free volume theory (Cohen and Turnbull, 1959Cohen M.H. Turnbull D. Molecular transport in liquids and glasses.J. Chem. Phys. 1959; 31: 1164-1169Crossref Scopus (3409) Google Scholar; Turnbull and Cohen, 1961Turnbull D. Cohen M.H. Free-volume model of the amorphous phase: glass transition.J. Chem. Phys. 1961; 34: 120-125Crossref Scopus (1040) Google Scholar, Turnbull and Cohen, 1970Turnbull D. Cohen M.H. On the free-volume model of the liquid-glass transition.J. Chem. Phys. 1970; 52: 3038-3041Crossref Scopus (682) Google Scholar). In fact, the agreement between free area theory and experiment is not only qualitative but also quantitative, as shown in Fig. 1, which presents data and theoretical curves for diffusion in pure DMPC and DMPC/Chol (χcho = 0.30, 0.40, and 0.50) as a function of temperature (Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google Scholar). The theoretical curves were obtained by fitting the equationDL=A(a1/2)e−ao/afe−Ea/kT,(1) to the experimental data using a simple least-squares analysis. The only free parameters in this procedure were the average cross-sectional, hard-core area (equivalent to the van der Waals volume) of cholesterol (aocho), which was subtracted from the total area to obtain the free area (af), and the activation energy (Ea). The preexponential factor depends on the square root of the area over which diffusion occurs as described in detail by Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google Scholar. We found that a value for aocho=26.6Å2, for all DMPC/Chol compositions examined (χcho = 0.30, 0.40, and 0.50), yielded very good agreement with the experimental data; and that Ea = 2.7 kcal/mol for pure DMPC, and 1.9, 2.1, and 2.5 kcal/mol for DMPC/Chol 70:30, 60:40, and 50:50, respectively, gave the best fits. It is interesting that the value of 26.6 Å2 is exactly the same as determined recently by MD simulations, which yielded 27 ± 1 Å2 (Hofsaß et al., 2003Hofsaß C. Lindahl E. Edholm O. Molecular dynamics simulations of phospholipid bilayers with cholesterol.Biophys. J. 2003; 84: 2192-2206Abstract Full Text Full Text PDF PubMed Scopus (414) Google Scholar; Khelashvili and Scott, 2004Khelashvili G.A. Scott H.L. Combined Monte Carlo and molecular dynamics simulation of hydrated 18:0 sphingomyelin-cholesterol lipid bilayers.J. Chem. Phys. 2004; 120: 9841-9847Crossref PubMed Scopus (70) Google Scholar). Such nearly perfect agreement is certainly fortuitous, but it indicates that the value we arrived at is entirely reasonable. However, Falck et al., 2004Falck E. Patra M. Karttunen M. Hyvönen M.T. Vattulainen I. Lessons of slicing membranes: interplay of packing, free area, and lateral diffusion in phospholipid/cholesterol bilayers.Biophys. J. 2004; 87: 1076-1091Abstract Full Text Full Text PDF PubMed Scopus (239) Google Scholar write, "it seems reasonable to expect that Ea should increase with cholesterol content. Experimental results (Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google Scholar) do support this idea but are partly contradictory. This is, however, probably due to the fitting procedure used." First, we cannot discern any contradiction in our experimental results: there are no two measurements of the same observable that yield different values. If we understand Falck et al. correctly, they are not questioning the fitting method itself (least squares) but the possible effects of the preexponential factor and the use of constant (temperature-independent) values for the hard-core, cross-sectional areas of DMPC (aopc) and cholesterol (aocho). In our work, aopc was taken as the close-packed area per lipid in gel state DMPC (45 Å2) and aocho was an adjustable parameter in the fits. Slightly different choices for the preexponential factor have a very minor effect because of its weak (square root) dependence on the area. Reasonable variations in this term lead to no more than ∼0.1 kcal/mol changes in the values obtained for Ea for the different systems that we examined and are insufficient to alter the ranking of Ea values in these four mixtures. Indeed, we noted that Ea for DMPC and DMPC/Chol 50:50 are essentially the same (Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google Scholar). With the same Ea, it was then suggested that the effect of cholesterol content in the ℓo phase (50:50 mixture) should be equivalent to a shift in temperature, which was shown to be the case (Fig. 2). The meaning of a minimum in Ea for a mixture with χcho = 0.3 deserves some discussion, which is postponed until the next section. Before concluding this summary we should note that the data of Filippov et al., 2003Filippov A. Orädd G. Lindblom G. The effect of cholesterol on the lateral diffusion of phospholipids in oriented bilayers.Biophys. J. 2003; 84: 3079-3086Abstract Full Text Full Text PDF PubMed Scopus (354) Google Scholar yield a different temperature dependence as a function of cholesterol, with a monotonically increasing Ea with cholesterol content in DMPC/Chol. However, their Ea values were obtained with simple Arrhenius plots, not with Eq. 1; therefore, in this form, they cannot be directly compared with ours. The MD simulations of Falck et al., 2004Falck E. Patra M. Karttunen M. Hyvönen M.T. Vattulainen I. Lessons of slicing membranes: interplay of packing, free area, and lateral diffusion in phospholipid/cholesterol bilayers.Biophys. J. 2004; 87: 1076-1091Abstract Full Text Full Text PDF PubMed Scopus (239) Google Scholar and their analysis by "slicing" the bilayer at various levels along the normal have made clear an important difficulty of free area theory when applied to diffusion in lipid bilayers: the fact that the free volume is not constant across the bilayer height. Therefore, the assignment of a value to aopc and aocho is conceptually complicated. Free area theory defines an average cross-sectional area for a lipid and treats diffusion in the bilayer as two-dimensional, which is not strictly correct. Movement of the lipids into free volumes at different levels along the bilayer normal would reasonably be expected to contribute to diffusion, probably softening the barriers to displacements along the bilayer plane. Essentially, the free area model ignores all these complications and aopc and aocho are then, to some extent, operational parameters. Apart from that conceptual difficulty with free area theory (which we share), Falck et al. appear to have two major problems when comparing their MD simulations with our experiments and their interpretation using free area theory: 1), the magnitude of the decrease in the diffusion coefficient when Chol content is increased from χcho ≈ 0 to χcho ≈ 0.30; and 2), our observation of a minimum in Ea for DMPC/Chol 70:30, compared to pure DMPC and DMPC/Chol 60:40 and 50:50. With regard to the first problem, Falck et al. base their conclusions on the fact that their MD simulations show a reduction of a factor of 10 in the lipid diffusion coefficient (DL) when χcho is increased from 0.047 to 0.297 (Falck et al., 2004Falck E. Patra M. Karttunen M. Hyvönen M.T. Vattulainen I. Lessons of slicing membranes: interplay of packing, free area, and lateral diffusion in phospholipid/cholesterol bilayers.Biophys. J. 2004; 87: 1076-1091Abstract Full Text Full Text PDF PubMed Scopus (239) Google Scholar). However, if free area theory were correct, they calculate that DL should be reduced by a factor of 3 at most. As shown above, in experimental measurements, the effect of cholesterol content on DL is consistently a reduction by a factor of 2–3, up to χcho ≈ 0.50, for all measurements including those of Korlach et al., 1999Korlach J. Schwille P. Webb W.W. Feigenson G.W. Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy.Proc. Natl. Acad. Sci. USA. 1999; 96: 8461-8466Crossref PubMed Scopus (720) Google Scholar for χcho = 0.30. Therefore, experimentally, the ratio of DL in the ℓd to the ℓo phase agrees very well with the prediction of free area theory, as estimated by Falck et al., 2004Falck E. Patra M. Karttunen M. Hyvönen M.T. Vattulainen I. Lessons of slicing membranes: interplay of packing, free area, and lateral diffusion in phospholipid/cholesterol bilayers.Biophys. J. 2004; 87: 1076-1091Abstract Full Text Full Text PDF PubMed Scopus (239) Google Scholar. In support of their MD results, Falck et al. cite a measurement by Korlach et al., 1999Korlach J. Schwille P. Webb W.W. Feigenson G.W. Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy.Proc. Natl. Acad. Sci. USA. 1999; 96: 8461-8466Crossref PubMed Scopus (720) Google Scholar in DLPC/Chol using fluorescence correlation spectroscopy (FCS), which gives a reduction of 10 upon addition cholesterol to a final χcho = 0.60. This decrease is a feature of the data of Korlach et al., 1999Korlach J. Schwille P. Webb W.W. Feigenson G.W. Characterization of lipid bilayer phases by confocal microscopy and fluorescence correlation spectroscopy.Proc. Natl. Acad. Sci. USA. 1999; 96: 8461-8466Crossref PubMed Scopus (720) Google Scholar for χcho = 0.60, but has not been observed by other investigators. To the best of our knowledge, all other studies have shown that above χcho = 0.30 the lipid diffusion coefficient does not vary much. In any case, the comparison made by Falck et al., 2004Falck E. Patra M. Karttunen M. Hyvönen M.T. Vattulainen I. Lessons of slicing membranes: interplay of packing, free area, and lateral diffusion in phospholipid/cholesterol bilayers.Biophys. J. 2004; 87: 1076-1091Abstract Full Text Full Text PDF PubMed Scopus (239) Google Scholar was with MD simulations of dipalmitoylphosphatidylcholine (DPPC)/Chol containing χcho = 0.297, so the relevant experimental data are those for χcho = 0.30, not 0.60; and at χcho = 0.30 DL is reduced by a factor of 3 (as predicted by the free area model), not 10 (as predicted by the MD simulations). Why then do the MD simulations show a stronger effect of Chol on DL? One possibility is that this is due to the timescale of the simulations, which was 100 ns (Falck et al., 2004Falck E. Patra M. Karttunen M. Hyvönen M.T. Vattulainen I. Lessons of slicing membranes: interplay of packing, free area, and lateral diffusion in phospholipid/cholesterol bilayers.Biophys. J. 2004; 87: 1076-1091Abstract Full Text Full Text PDF PubMed Scopus (239) Google Scholar). This is a long time for an MD simulation, but is still short for diffusion. With a typical DL = 5 × 10−8 cm2s−1, the area explored by a lipid molecule in 100 ns is 200 Å2, which is only three times the average cross-sectional area per phospholipid in a fluid bilayer, ∼65 Å2. Another way of looking at the problem is that this timescale allows only for three "jumps" if lipid diffusion is viewed as a random walk on a lattice. This is certainly not long-range diffusion. In our opinion, this is probably the main the reason for the apparent discrepancy between the MD simulations and the experimental data obtained with techniques that measure long-range diffusion, such as FRAP, FCS, and pulsed field gradient (pfg)-NMR. The differences in measurements of long- and short-range diffusion have been addressed previously (Vaz and Almeida, 1991Vaz W.L.C. Almeida P.F.F. Microscopic versus macroscopic diffusion in one-component fluid phase lipid bilayer membranes.Biophys. J. 1991; 60: 1553-1554Abstract Full Text PDF PubMed Scopus (82) Google Scholar). In addition, could it be that the force fields currently available for MD simulations do not correctly model the water-membrane interfacial region? Falck et al., 2004Falck E. Patra M. Karttunen M. Hyvönen M.T. Vattulainen I. Lessons of slicing membranes: interplay of packing, free area, and lateral diffusion in phospholipid/cholesterol bilayers.Biophys. J. 2004; 87: 1076-1091Abstract Full Text Full Text PDF PubMed Scopus (239) Google Scholar point out that their simulations, as well as any other united-atom MD simulations, cannot reproduce the behavior of the experimental 2H-NMR order parameter for the deuterons on the second carbon of the sn-2 chain (Sankaram and Thompson, 1990aSankaram M.B. Thompson T.E. Modulation of phospholipid acyl chain order by cholesterol: a solid-state 2H-nuclear magnetic resonance study.Biochemistry. 1990; 29: 10676-10684Crossref PubMed Scopus (224) Google Scholar; Seelig and Seelig, 1975Seelig A. Seelig J. Bilayers of dipalmitoyl-3-sn-phosphatidylcholine: conformational differences between the fatty acid chains.Biochim. Biophys. Acta. 1975; 406: 1-5Crossref PubMed Scopus (163) Google Scholar), which are near the interface. A third possibility is that the experimental, long-range DL in PC/Chol systems is affected by phospholipid–Chol complex formation, which could occur on timescales beyond the reach of the current MD simulations. With regard to the second problem, the minimum in Ea for DMPC/Chol 70:30, which results from the analysis of our diffusion data using free area theory (Eq. 1), Falck et al., 2004Falck E. Patra M. Karttunen M. Hyvönen M.T. Vattulainen I. Lessons of slicing membranes: interplay of packing, free area, and lateral diffusion in phospholipid/cholesterol bilayers.Biophys. J. 2004; 87: 1076-1091Abstract Full Text Full Text PDF PubMed Scopus (239) Google Scholar find this result unexpected and attribute it to an incompleteness of free area theory. This is possible. Perhaps what appears as an activation energy in that analysis has contributions that the theory does not treat or does not treat adequately. As a type of mean-field theory, its treatment of fluctuations, which are critical for diffusion, is certainly not complete. Nevertheless, with all its imperfections, free area theory has successfully described lipid diffusion in a quantitative way in the experimental systems that we have examined (Vaz et al., 1985Vaz W.L.C. Clegg R.M. Hallmann D. Translational diffusion of lipids in liquid-crystalline phase phosphatidylcholine multibilayers: a comparison of experiment with theory.Biochemistry. 1985; 24: 781-786Crossref PubMed Scopus (273) Google Scholar; Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google Scholar). The theory is certainly simple; however, simplicity in a theory is not necessarily a weakness. The real test of a theory is its ability to describe experimental data. As stated by Feynman et al., 1963Feynman R.P. Leighton R.B. Sands M. The Feynman Lectures on Physics. Vol. 1. Addison-Wesley, Reading, MA1963Google Scholar, "The principle of science, the definition, almost, is the following: the test of all knowledge is experiment. Experiment is the sole judge of scientific 'truth'." Yet, another possibility is that the minimum in Ea for DMPC/Chol 70:30 is real and reflects some important property of the system. If phospholipid/cholesterol systems are understood on the basis of a phase diagram, χcho = 0.30 essentially corresponds to the composition of the ℓo phase in equilibrium with the ℓd phase in the two-phase region. This may not be a coincidence and may reflect some special property of 2:1 PC/Chol mixtures. If an interpretation of the behavior of phospholipid/cholesterol systems in terms of complex formation is preferred, as proposed by McConnell and collaborators in recent work (see, for a review, McConnell and Radhakrishnan, 2003McConnell H.M. Radhakrishnan A. Condensed complexes of cholesterol and phospholipids.Biochim. Biophys. Acta. 2003; 1610: 159-173Crossref PubMed Scopus (357) Google Scholar) this composition corresponds to a pressure cusp (minimum) in the phase diagrams of phospholipid/Chol systems, which has been interpreted by them as indicative of the formation of a phospholipid/cholesterol 2:1 condensed complex. An interesting observation by Chong, 1994Chong P.L.-G. Evidence for regular distribution of sterols in liquid crystalline phosphatidylcholine bilayers.Proc. Natl. Acad. Sci. USA. 1994; 91: 10069-10073Crossref PubMed Scopus (131) Google Scholar, on the basis on our calculated mean areas per DMPC as a function of cholesterol content (Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google Scholar), is that the average value of a DMPC cross-sectional area per chain at 35°C is reduced from 29.5 Å2 in pure DMPC to 26.7 Å2 in 70:30 DMPC/Chol. This is exactly the same as the value found for aocho, 26.6 Å2, which, because it corresponds to a rigid molecule (cholesterol) is not expected to change with temperature (Chong, 1994Chong P.L.-G. Evidence for regular distribution of sterols in liquid crystalline phosphatidylcholine bilayers.Proc. Natl. Acad. Sci. USA. 1994; 91: 10069-10073Crossref PubMed Scopus (131) Google Scholar; McConnell and Radhakrishnan, 2003McConnell H.M. Radhakrishnan A. Condensed complexes of cholesterol and phospholipids.Biochim. Biophys. Acta. 2003; 1610: 159-173Crossref PubMed Scopus (357) Google Scholar). Therefore, packing may be especially good and the exchange between PC chains and cholesterol may be especially easy at χcho = 0.30. This could be reflected in an smaller apparent Ea. Finally, as we have suggested (Almeida et al., 1992Almeida P.F.F. Vaz W.L.C. Thompson T.E. Lateral diffusion in the liquid phases of dimyristoylphosphatidylcholine/cholesterol lipid bilayers: a free volume analysis.Biochemistry. 1992; 31: 6739-6747Crossref PubMed Scopus (523) Google Scholar), these variations in Ea may reflect changes in hydration of the bilayer, which may not be monotonic with χcho when comparing one phase with the other (ℓd and ℓo), although they would be expected to be monotonic within each phase when the cholesterol content is changed, as is observed. This work was supported in part by grant GM59205 from the National Institutes of Health to the University of Virginia/PFFA.
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