Polarity and permeation profiles in lipid membranes

Phospholipids were from Avanti Polar Lipids and cholesterol was from Merck. Spin-labeled phosphatidylcholines, n-PCSLs {1-acyl-2-[n-(4,4-dimethyloxazolidine-N-oxyl)stearoyl]-sn-glycero-3-phosphocholine}, were synthesized as described in Marsh and Watts (9).

Phospholipids with or without 50 mol % cholesterol were dissolved in dichloromethane with 1 mol % of the desired n-PCSL (n = 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, or 16). After removal of organic solvent and vacuum drying, the lipids were dispersed in 10 mM Tris 0.1 M KCl (pH 8.0) buffer. For unsaturated lipids, samples and buffer were saturated with argon. Hydrated samples were pelleted in 1-mm diameter glass capillaries. These were then accommodated in a standard quartz EPR tube that contained light silicone oil for thermal stability. See ref. 10 for further details.

Spectra were recorded on a Varian Century-Line 9-GHz spectrometer at 5° intervals from 25°C to 70°C. Samples were thermostated by nitrogen gas flow. Temperature was measured with a fine-wire thermocouple adjacent to the sample at the top of the cavity. Isotropic ¹⁴N-hyperfine constants were determined from the relation: where A_⊥ and A_∥ are the hyperfine constants determined with the magnetic field perpendicular and parallel, respectively, to the membrane normal. The latter were determined from the outer and inner spectral hyperfine splittings with corrections given in Marsh (11). The anisotropic spectra were recorded at temperatures sufficiently high that the spectral splittings were unaffected by slow motional contributions (10). For spectra of spin labels close to the terminal methyl group of the lipid chains, the spectral anisotropy is small and not well resolved. In these cases, a temperature sufficiently high to give totally isotropic spectra was used so that the spectral hyperfine splittings are equal to a\( \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\) itself. For both the former and latter cases, the experimental criterion for validity is that the (effective) values derived for a\( \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\) should have little or no temperature dependence. Typically, measurements from 5–10 spectra recorded at 5°C intervals in this range were averaged. Errors in the mean value were 0.05–0.1 G, or less, depending on lipid and spin-label position. Measurements used were confined to a single fluid or liquid-ordered phase, and there was no hint of any pronounced spin-spin broadening in the spectra that might indicate inhomogeneities in probe distribution.

Values of the isotropic hyperfine coupling constant, a\( \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\), of spin-labeled glycerophospholipids with the nitroxide group at position n in the sn-2 chain (n-PCSL) were obtained from the EPR spectra of the n-PCSLs at probe amounts in fluid phospholipid bilayer membranes as described in Materials and Methods (see also refs. 11 and 12). A typical transmembrane profile of the isotropic hyperfine splitting constants is given in Fig. 1 for n-PCSL in fluid dipalmitoyl phosphatidylcholine (DPPC) membranes. The profile for liquid-ordered DPPC membranes that contain equimolar cholesterol is also shown in the same figure. There are very significant differences between the polarity profiles of DPPC membranes with and without cholesterol. Nevertheless, both profiles have the same overall trough-like shape. Corresponding data were obtained for dimyristoyl phosphatidylcholine (DMPC) membranes and for 1-palmitoyl-2-oleoyl and dioleoyl phosphatidylcholine (POPC and DOPC) membranes, with and without equimolar cholesterol. These lipids also produced trough-like profiles in the fluid phase, with qualitatively similar modifications by cholesterol, but with significant differences between saturated and unsaturated lipids (see below).

The trough-like dependence of the isotropic ¹⁴N-hyperfine-coupling constant, a\( \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\), on spin-label position, n, in the lipid chain (Fig. 1) is of the following form: where a\( \begin{equation*}{\mathrm{_{o,1}^{N}}}\end{equation*}\) and a\( \begin{equation*}{\mathrm{_{o,1}^{N}}}\end{equation*}\) are the limiting values of a\( \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\) at the polar headgroup and terminal methyl ends of the chain, respectively, and λ is an exponential decay constant. Eq. 2 applies to all n, and n_o is the value of n at the point of maximum gradient, corresponding to a\( \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\)(n_o) = ½(a\( \begin{equation*}{\mathrm{_{o,1}^{N}}}\end{equation*}\) + a\( \begin{equation*}{\mathrm{_{o,2}^{N}}}\end{equation*}\)). For large n, the dependence becomes a simple exponential. The profile given by Eq. 2 is exactly antisymmetric about the position n_o. A physically plausible asymmetry could be introduced, requiring a further adjustable parameter. To within the sensitivity of the data, however, this refinement is not justified.

Eq. 2 corresponds to the so-called Boltzmann sigmoidal form, and has a relatively straightforward thermodynamic interpretation. It corresponds to a normalized two-phase distribution, ≈exp[−(n − n_o)/λ], between outer and inner regions of the membrane that are defined by n < n_o and n > n_o, respectively. The free energy of transfer, (n − n_o)k_BT/λ, increases linearly with the distance, n − n_o, into the inner region. It seems intuitively reasonable to identify these two membrane regions with the interfacial region and hydrocarbon core, respectively, that were defined by Wiener and White (8) by using diffraction methods. A quantitative comparison with the latter results is given later.

The fitted curves in Fig. 1 demonstrate that Eq. 2 provides an adequate description of the polarity profiles for fluid phospholipid membranes both in the presence and in the absence of cholesterol. The parameters determined by nonlinear least-squares fitting are given in Table 1, which includes data from all lipid bilayer membranes studied. Data are also given for bovine chromaffin granule membranes and bilayers of their extracted lipids derived from measurements with spin-labeled stearic acid, n-SASL [n-(4,4-dimethyloxazolidine-N-oxyl)stearic acid].

The parameters for both DMPC and DPPC membranes without cholesterol are rather similar, particularly with regard to the limiting values (a\( \begin{equation*}{\mathrm{_{o,1}^{N}}}\end{equation*}\) and a\( \begin{equation*}{\mathrm{_{o,2}^{N}}}\end{equation*}\)) and the values of n_o (≈8) that characterize the steepest part of the polarity profile (Table 1). The 9–10-cis unsaturated bond of the oleoyl chain in POPC and DOPC modifies the profile somewhat, relative to that of DPPC bilayers with fully saturated chains. The midpoint position of the profile (n_o ≈ 8) is similar, but the width of the transition region (λ = 1.0) is significantly broadened. (In contrast, the lower order of unsaturated lipid bilayers would tend to increase the effective values of both n_o and λ when expressed in terms of chain segment position.) In addition, the polarity in regions closer to the membrane surface is higher for the unsaturated lipids. The large difference in polarity reported between saturated and unsaturated lipids in the central region of frozen membranes (3) is not found, however, for fluid membranes.

In membranes that contain equimolar cholesterol, which includes chromaffin granule membranes and their extracted lipids, the point of steepest slope is shifted away from the membrane surface to n_o ≈ 9–10 CH₂ units. Concomitantly, the total extent of the profile is increased to higher polarities closer to the membrane surface, and lower polarities at the membrane mid-plane. These consistent changes are undoubtedly associated with the well-known ordering effect of cholesterol on fluid lipid chains, in addition to a spacing function at the polar headgroup region of the lipids. Qualitatively similar effects of cholesterol have been observed previously on the polarity profiles in frozen membranes (3).

The polarity profile registered by the spin-label isotropic hyperfine splitting constants can, at least in part, be related to water penetration into the lipid membranes. Experiments in aprotic solvents with increasing concentrations of H-bond donor (15) have revealed a linear dependence of a\( \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\) on increasing concentration of water, after allowance for changes in dielectric constant. The complete polarity dependence of the isotropic ¹⁴N-hyperfine coupling constant can be expressed as follows (see, for example, refs. 12 and 15): where ɛ is the local dielectric constant of the medium and p is the local proton donor concentration. The values of the scaling parameter K_v and the limiting value a\( \begin{equation*}{\mathrm{_{o}^{{\varepsilon}=1}}}\end{equation*}\) depend on the type of nitroxide. For the oxazolidine-N-oxyl radicals considered here, K_v = 0.64 G and a\( \begin{equation*}{\mathrm{_{o}^{{\varepsilon}=1}}}\end{equation*}\) = 13.85 ± 0.09 G (12). The polarity profiles parametrized in Table 1 can be related to membrane permeation profiles for water molecules by means of the last term on the right in Eq. 3. In the absence of H-bonding (i.e., p = 0) the isotropic hyperfine constants predicted from Eq. 3 are a\( \begin{equation*}{\mathrm{_{o}^{{\varepsilon}=80}}}\end{equation*}\) = 14.5 G and a\( \begin{equation*}{\mathrm{_{o}^{{\varepsilon}=2}}}\end{equation*}\) = 14.1 G in media with dielectric constants ɛ = 80 (water) and ɛ = 2 (hydrocarbon), respectively. These polarity-corrected values are used as references to determine the H-bond contribution to a\( \begin{equation*}{\mathrm{_{o,1}^{N}}}\end{equation*}\) and a\( \begin{equation*}{\mathrm{_{o,2}^{N}}}\end{equation*}\), respectively, in the outer and inner regions of the membrane. The part of the polarity profile attributed to water penetration is then expressed in terms of the fractional increment relative to pure water, for which a_o = 15.7 G. The corresponding values of water penetration, p₁ and p₂, that refer to the extremes of the a\( \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\)-profile are given in Table 2. It should be emphasized that these effective values depend on the limiting assumptions that have been made for the local dielectric constant, which is difficult to estimate reliably. They are, however, in some sense a measure for the local water activity that must be in equilibrium with that of the unlabeled lipid environment.

It is seen from Table 2 that, in the presence of 50 mol % cholesterol, relatively little water is present at the center of the membrane, whereas as in fluid bilayer membranes without cholesterol an appreciable amount of water permeates to the mid-plane of the membrane. This result correlates with the reduced water permeability of lipid membranes that contain cholesterol (16, 17). At the polar headgroup end of the hydrophobic region of the membrane, the extent of water permeation is considerably higher for unsaturated lipids, as seen by the substantially increased values of p₁.

The permeability coefficient, P, of a membrane to polar solutes is related to the transmembrane polarity or permeation profile by Diamond and Katz (18). where k′ and k" are the rate constants for solute entry at the two faces of the membrane and 2d is the membrane thickness of the hydrophobic region. The permeability barrier of the latter is given by the integral in Eq. 4, where K(x) and D(x) are the local partition coefficient and diffusion coefficient, respectively, of the solute at distance x into the membrane. From Eq. 3, it is reasonable to assume that the product K(x)D(x) has a transmembrane profile of the form given in Eq. 2. The value of K(x) is proportional to the local water concentration, p, and that of K_h in Eq. 3 will depend on the local diffusion-controlled on-rate, specified by D(x) (see ref. 15). For the case of oxygen and paramagnetic complexes, considered later, the accessibilities measured from spin-label relaxation enhancements are explicitly proportional to the K(x)D(x), concentration-diffusion product (19).

Performing the integration in Eq. 4 by using the profile given by Eq. 2, yields the following contribution, δ(1/P), to the permeability barrier. where d_o is the distance corresponding to chain position n_o, and λ is also expressed as a distance. K₁D₁ and K₂D₂ are the partition coefficient and diffusion coefficient products at the beginning of the apolar region and at the center of the membrane, respectively. The first term in square brackets on the right side of Eq. 5 represents the normal diffusive resistance of a uniform membrane of thickness 2d that is characterized by a partition coefficient K₁ and a diffusion coefficient D₁. The remaining term represents the additional resistance contributed by the permeability barrier. From the spin-label results, the ratio K₁D₁/K₂D₂ can be approximated by the values of p₁/p₂ from Table 2. Together with the data of Table 1, the effective increase in membrane thickness by the permeability barrier that is predicted by the second term on the right of Eq. 5 corresponds to ≈12 (28) CH₂ units for DPPC (POPC) membranes. This value is effectively increased by a further 38 (54) CH₂ units on admixture of equimolar cholesterol. A value of d corresponding to 17 (17.6) CH₂ units (including terminal methyl contacts) was used for these estimates. The ratio of permeabilities with and without cholesterol is then predicted to be 0.54 in both cases, assuming that the barrier given by Eq. 5 is rate limiting. This prediction is in reasonable agreement with experiments on water permeability, which is reduced by ≈50% on addition of equimolar cholesterol (16, 20). Finally, an order of magnitude estimate of the size of the permeability barrier to water can be made taking values of K₁ = 6.4 × 10⁻⁵ and D₁ = 5 × 10⁻⁵ cm²⋅s⁻¹ from measurements on water partitioning into hexadecane (21, 22). With an average increment of ≈0.1 nm per methylene group (23), this yields a value of P ≈ 5–7 × 10⁻³ cm⋅s⁻¹, which is of comparable size to the water permeabilities found experimentally (20, 24, 25).

Water permeation profiles might be expected to be mirrored by those of other small polar solutes. In fact, the permeation profile of apolar molecular oxygen, which is preferentially concentrated in the hydrophobic interior of lipid membranes, is also remarkably similar to the polarity profiles presented in Fig. 1 (19). The permeation profile understandably has the opposite sense, however, to that for the polarity or permeation of water. The oxygen permeation profile determined by the paramagnetic relaxation enhancement of spin-labeled phospholipids (see ref. 26) is given in Fig. 2. This may be well fitted by an expression analogous to Eq. 2 with a\( \begin{equation*}{\mathrm{_{o,2}^{N}}}\end{equation*}\)> a\( \begin{equation*}{\mathrm{_{o,1}^{N}}}\end{equation*}\). Significantly, the value obtained for n_o (≈7.8) is that characteristic of cholesterol-free membranes determined above from the polarity profile characterized by the spin-label isotropic hyperfine splitting, a\( \begin{equation*}{\mathrm{_{o}^{N}}}\end{equation*}\) (cf. Fig. 1). The extension into the lipid headgroup region of the fit in Fig. 2 is justified only to within the relatively limited amount of data available in this region. Polarity profiles from frozen membranes of unsaturated lipids (3) tend also to support such an extrapolation.

In contrast, the permeation profiles for polar paramagnetic ion complexes differ significantly from those for the polarity profiles that are given in Fig. 1. For chromium oxalate (Fig. 2), the permeation profile determined by paramagnetic relaxation enhancement of the spin-labeled lipids is better approximated by a simple exponential dependence. (See also data for nickel acetyl acetonate in ref. 7.) This positional dependence corresponds to that described by Eq. 2 for n_o ≪ n, i.e., in this case, the transition point determined by n_o lies outside the hydrophobic region of the membrane. It therefore follows that, in the case of polar paramagnetic ion complexes, the free energy of membrane permeation has an approximately linear dependence on penetration distance (cf. ref 7).

In general, however, the permeation free energy that corresponds to the concentration profile given by Eqs. 2 and 3, e.g., for water or oxygen, is not a linear function of the depth of penetration into the membrane. The linearity observed in the logarithm of the ratio of accessibilities to oxygen and paramagnetic complexes (7) therefore must be dominated by the exponential dependence for the paramagnetic complex (Fig. 2). This ratio method has proved extremely useful for determining vertical positions within the membrane, particularly in site-directed spin-labeling. Fitting the profiles for the accessibilities to oxygen and paramagnetic complexes separately, as done here in Fig. 2, has potential for improving the precision of such determinations.

Up to this point, the representation of the polarity and permeation profiles has been given in terms of the C-atom position in the phospholipid sn-2 acyl chain. In fluid lipid bilayer membranes not containing cholesterol, the mean C–C separation projected onto the membrane normal is ≈0.1 nm per methylene segment (ref. 23). This conversion may be used to express the profiles in terms of transbilayer separations. In fact, the effective spin-label positions n = −3.5 and n = −9 given in Fig. 2 have been derived in this way from the positions defined in the original work (26). To obtain the entire transbilayer profile, it is necessary to allow for the separation of the terminal methyl groups between the apposing monolayers. From the crystal structure of dilauroyl phosphatidylethanolamine (27), this separation is estimated as ≈0.55 nm, allowing also for the 1.5 CH₂ units offset between the sn-1 and sn-2 chains. For fluid phospholipid bilayers with C-18 chains, the width of the hydrophobic barrier between the points specified by n_o is then estimated as 2.55 nm. For comparison, the dynamic thickness of the hydrocarbon core of fluid DOPC bilayers, as represented by time-averaged group distributions from diffraction measurements, is given as 2.86 nm (8). This value was determined from samples with relatively low water content. Allowing for the latter will bring the two values into even closer proximity. Correspondingly, the polarity profile mapped out by the spin-labeled lipid chains correlates with the inner section of the partial charge density profile of DOPC bilayers calculated by White and Wimley (6). The latter was obtained from Gaussian group distributions (3 for all CH₂ groups) that were fitted to diffraction data.

It is further noted that the chain region before the principal hydrophobic barrier (i.e., up to n = n_o) is confined entirely to the plateau region of the segmental chain order parameters observed by ²H NMR (28). This means that the shape of the polarity profile will largely be preserved on translating from a chain-position scale (as in Fig. 1) to a transbilayer distance scale. Foreshortening of the distance profile, relative to the chain-position profile, occurs in the inner region, beyond the order-parameter plateau. Here a_o has achieved an almost constant, low value. For the same reason, the increased width in distribution of segment position toward the end of the chain is also unlikely to bias the profile unduly.

Measurements of the accessibility to oxygen of spin labels attached to cysteine residues that are systematically stepped throughout the sequence of the first transmembrane segment of the SKC1 K⁺-channel from Streptomyces lividans (29) provide a good example of the application to site-directed spin-labeling. The accessibilities that are determined from the relaxation enhancement by oxygen of the single spin-labeled cysteine mutants are given in Fig. 3, as a function of residue position in the primary sequence. This transmembrane domain is situated at the periphery of the channel, exposed to lipid. The oxygen accessibilities display an α-helical periodicity between the lipid-facing and the interior-facing residues.

The accessibility maxima in Fig. 3 map out the oxygen concentration profile in the lipid regions immediately surrounding the protein. These have a dependence on residue position that is similar to Eq. 2 for each side of the membrane. Largest oxygen concentration is in the middle of the membrane (residues 34–38) and lowest oxygen concentration at the two interfacial regions (residues 22 and 50). Because all residues are not fully exposed to oxygen, the oxygen profile envelope defined by these measurements (dashed lines in Fig. 3) is relatively coarse-grained. For this reason the approximate profile was first established by fitting Eq. 2 to the local maxima, for each side of the membrane separately. The resulting profiles were then refined by fitting the following expression, which is an extended version of Eq. 2 that allows for the helical periodicity, to all data points: where the sinusoidal term represents the α-helical periodicity of 3.6 residues per turn, with a phase offset δ_o, and the constant Π_o is the oxygen accessibility of the inward-facing residues. The solid lines in Fig. 3 give the fits to Eq. 6. For the N-terminal side of the membrane (residues 22–38) the fitting parameters of interest are n_o = 32.1 ± 1.2 and λ = 0.77 ± 0.75 residues. For the C-terminal side of the membrane (residues 34–52), the corresponding values are: n_o = 41.8 ± 1.2 and λ = 1.5 ± 1.1 residues. It is seen from Fig. 3 that the region of overlap (residues 34–38) between the two halves of the membrane matches reasonably well for the two independent fits.

Comparison can be made with the measurements on lipid bilayer membranes alone, using spin-labeled lipids. The distance between midpoints of the oxygen profile that are specified by n_o is 9.6 ± 2.4 residues. The corresponding distance estimated above for a lipid bilayer with C-16 chains is 2.0–2.2 nm. The rise per residue of an α-helix is 0.15 nm, and the helices in SKC1 are known to be tilted, thus the maximal separation in the latter case is 1.44 ± 0.36 nm. Therefore the width of the oxygen profile at the lipid–protein interface of SKC1 appears significantly narrower than that in lipid bilayer membranes. Part of this difference might be attributable to foreshortening of the lipid chains toward the terminal methyl group. However, part is undoubtedly attributable also to the nonvanishing polarity of the transmembrane protein segments.

The values of the decay length λ, unfortunately, are not determined with great precision because of the coarse-graining that is associated with the α-helical modulation of the accessibilities. They correspond to values of λ = 0.12 ± 0.11 and 0.23 ± 0.17 nm for the N- and C-terminal faces of the membrane, assuming a rise of 0.15 nm per residue of an α-helix. This may be compared with values of ≈0.08–0.1 nm obtained for lipid bilayers by using lipid spin labels (Table 1). At least part of this difference is to be accounted for by the tilting of the helices. A tilt of 46° for the N-terminal section of the helix, and greater for the C-terminal section, would be required to bring the two sets of values into agreement. The tilt of the transmembrane segments determined from the x-ray structure of the SKC1 channel is ≈25° (30). It therefore seems likely that the oxygen profile at the lipid–protein interface is more diffuse than in protein-free bilayers. This result again is in accord with the increase in intramembrane polarity introduced by the transmembrane segments of the protein. For helix D of bacteriorhodopsin, the spread of the oxygen profile appears to be even larger (7).