INTRODUCTION

TOP ABSTRACT INTRODUCTION MATERIALS METHODS RESULTS DISCUSSION REFERENCES

A complete understanding of the physical properties of specific membrane lipids requires a determination of the phase structures that are formed by these lipids under defined conditions. Because the lipid phases of biological interest are fully hydrated liquid-crystal mesophases, such a structural measurement involves a determination of the electron density distribution of the lipid/water system from a small number of powder-pattern-averaged orders of x-ray diffraction. In this article, we describe such a structure determination method that is then applied to aqueous dispersions of various phosphatidylethanolamines (PEs). In an accompanying article to be published elsewhere (D. A. Mannock, R. N. A. H. Lewis, R. N. McElhaney, P. E. Harper, and S. M. Gruner, submitted for publication), these results will be used in a comparative study of PEs and diacyl--D-glucosyl-glycerols containing fatty acyl chains of various lengths and structures.

To illuminate the physical principles at work in these systems, it is important to study systems with a variety of chemical structures to differentiate between general physical behavior and physical behavior that varies with the lipid chemical structure. In this paper, we determine the structural parameters of seven PEs with hydrocarbon chains having different chemical structures, but the same effective chain length (ECL).

The ECL of a hydrocarbon chain is defined by the total number of carbons in the "main chain." For linear saturated and unsaturated fatty acyl groups, the ECL equals the total number of carbon atoms present, whereas for the branched fatty acyl chains, the ECLs equal the total number of carbon atoms minus those present in the branch(es). For -cyclohexyl fatty acyl groups, where three carbon atoms of the terminal six-membered ring actually form part of the main chain, the ECL is equal to the total number of carbon atoms present minus three.

Although the unit cell basis vector lengths (d-spacings) of both the lamellar liquid-crystalline (L) and inverted hexagonal phases (H_II) are readily measured, additional information about the specific chemical structures of these lipids may be used to compute the electron density reconstructions to determine such quantities as average lipid length (l) and water layer thickness (w and r). We first detail the theory and practice of this method of performing the reconstructions and then apply the method to various PEs. The results presented here also serve to correct earlier measurements (Lewis et al., 1989), in which some of the structural dimensions versus temperature were incorrect by as much as 10% due to a faulty temperature calibration arising from a voltage bias in the temperature controller.

	MATERIALS

TOP ABSTRACT INTRODUCTION MATERIALS METHODS RESULTS DISCUSSION REFERENCES

The seven PEs used in this study were 1,2-di-O-[cis-9,10-octadecenoyl("oleoyl")]-3-O-phosphatidylethanolamine-sn-glycerol (18:1c9-PE), 1,2-di-O-[trans-9,10-octadecenoyl("elaidoyl")]-3-O-phosphatidylethanolamine-sn-glycerol (18:1t9-PE), 1,2-di-O-[16'-ethyl-octadecanoyl]-3-O-phosphatidylethanolamine-sn-glycerol (20:0_eai-PE), 1,2-di-O-[17',17'-dimethyl-octadecanoyl]-3-O-phosphatidylethanolamine-sn-glycerol (20:0_dmi-PE), 1,2-di-O-[16'-methyl-octadecanoyl]-3-O-phosphatidylethanolamine-sn-glycerol (19:0_ai-PE), 1,2-di-O-[15-cyclohexyl-pentadecanoyl]-3-O-phosphatidylethanolamine-sn-glycerol (21:0_ch-PE), and 1,2-di-O-[17'-methyl-octadecanoyl]-3-O-phosphatidylethanolamine-sn-glycerol (19:0_i-PE). The numbers in the above abbreviated chemical nomenclature indicate the total number of carbon atoms in the hydrocarbon chain and the number, configuration, and position of any double bonds in the chain, whereas the subscripts indicate the type and position of the branches in the hydrocarbon chain (Lewis et al., 1989). The 18:1c9-PE and 18:1t9-PE were purchased from Avanti Polar Lipids (Alabaster, AL) and used as received. The remaining lipids were synthesized as described earlier (Lewis et al., 1989).

	METHODS

TOP ABSTRACT INTRODUCTION MATERIALS METHODS RESULTS DISCUSSION REFERENCES

Lipid molecular volumes

To determine the structural parameters of the various PEs studied, estimations of their molecular volumes are required. The volumes of 18:1c9-PE and 18:1t9-PE as a function of temperature and pressure have been measured by a combination of the method of neutral buoyancy in H₂O/D₂O mixtures (Nagle and Wilkinson, 1978) and high-pressure dilatometry (So et al., 1992). These methods require >100 mg of lipid, which is much more than the available supply of the other 18 carbon ECL PEs. Alternatively, the molecular volumes of the lipids can be estimated to the required accuracy by using the volumes of similar constituent hydrocarbons (see Table 1), along with the measured value for 18:1c9-PE and the assumption that the headgroup volumes of all the PEs are identical. For the temperature dependence, it is known that lipids like 18:1c9-PE and 18:1t9-PE in their L phases have a coefficient of expansion of V/V = 7 × 10⁴/°C and that the L/H_II phase transition involves a V/V of approximately 0.33% (So, 1992). Therefore, if the volume of a lipid is known at one temperature, the linear approximation given above can be used to determine the volume at any other temperature in the L portion of the phase diagram to an accuracy of better than 1% (So, 1992; So et al., 1993).

As a specific example and as a test of the accuracy of such an estimation, consider the two PCs for which the specific volumes are known, 15:0_i-PC (1.01 ml/g at 45°C; Yang et al., 1986) and 16:0-PC (1.004 ml/g at 45°C; Melchior et al., 1980). The molecular weights of 15:0_i-PC and 16:0-PC are 762.11 and 734.05, respectively, yielding volumes of 1278 and 1224 Å³, respectively. We can estimate the specific volume of 15:0_i-PC, v_15i-PC, by considering it to be the volume
which is in good agreement with the measured value of 1278 Å³. A similar calculation for 18:1t9-PE, starting from the measured value of 18:1c9-PE, yields a value that is within 2% of the measured value for 18:1t9-PE. Volumes for the other lipids are evaluated similarly and are presented in Table 2.

General electron density reconstruction theory

Our concern is with the L and the H_II phases, both of which are centrosymmetric. If one has a centrosymmetric unit cell (i.e., _e(r) = _e(r), where  is the electron density and r is the vector to the position in the unit cell), the electron density can be written as a Fourier series of cosines. With A_q being the Fourier coefficients and q the Fourier vector, the electron density, _e, as function of position r can be written,

(1)

where _avg is the average electron density. For a powder sample of crystals, one will see a pattern of concentric rings of diffraction, each ring corresponding to a Fourier component q of the electron density. The integrated intensity I_q of a ring is related to its Fourier coefficient A_q by

(1a)

where m is the multiplicity factor for the coefficient and the sin  factor is the Lorentz correction (see Warren, 1969). The multiplicity is the number of orientations of a crystal relative to the incoming x-rays that will yield a given reflection. The approximation sin    is made because all data are in the small angle region,  < 0.1.

In the small angle regime, the Lorentz correction (up to an overall scaling factor) is made by dividing the integrated intensities of the diffraction orders by the magnitude of the reciprocal lattice vector. For instance, the intensity of the second-order peak in the L phase is divided by 2. In the H_II phase, the reciprocal lattice vectors also form a hexagonal lattice, and so, from geometry, the magnitude of the vector (h, k) is (h² + hk + k²). Therefore, the (1, 1) peak in the H_II phase is divided by . (For more information on the Lorentz correction, see Warren (1969) and Turner (1990)). The peak intensity is divided by the multiplicity of the reflection. For example, in the H_II phase, the (1, 0) peak has the same magnitude and reciprocal vector length as the (0, 1), (1, 1), (1, 1), (1, 0), and (0, 1) peaks, and so has a multiplicity of 6. Therefore, the peak intensity of (1, 0) peak is divided by 6. For the L phase, all the peaks have a multiplicity of 1. For the H_II phase, the peaks (2, 1), (3, 1), (3, 2), and (4, 1) each have a multiplicity of 12 and the remaining peaks have a multiplicity of 6 (Turner, 1990).

This is almost enough information to reconstruct the electron density of the liquid crystals from x-ray diffraction. What is missing are the signs of the A_q, e.g., the relative phases of the diffracted orders. Several methods have been developed to deal with this difficulty. One method is to construct a model of the electron density consistent with a known lipid chemical structure and then to pick the phasing that comes closest to reproducing the model, subject to the constraint that the rejected choices are clearly unphysical. Conversely, one can Fourier transform the model and then use the resulting phases in the reconstruction. Extensive work in modeling lamellar structures has been done by Wiener et al. (1992) and the H_II structure has been modeled by Turner and Gruner (1992). Another means to determine the phases is the swelling method, in which structures at slightly different hydrations are compared. Because the electron density should only be shifted slightly by a small change in hydration, it is a reasonable assumption that the integrated difference of the square of the electron densities should be at a minimum for the proper phasing. This method was used by Stamatoff and Krimm (1976) for lamellar systems and was extended to H_II systems by Turner (1990) and Turner and Gruner (1992). Yet another method is the technique of Luzzati and co-workers, where _e is the electron density. They stated that, if one compares two structures of identical chemical composition, the value of should be the same for both. If one structure has a known phasing, this can be used to determine the phasing for the other structure. A recent example of this method is contained in Mariani et al. (1990). A new phasing technique, the methyl trough search, has recently been described by our groups (Harper and Gruner, 2000; Harper et al., 2000).

Lamellar phase reconstruction

A first step in determining a proper phasing for the L system is to construct a simple model of what a correct phasing should yield, based on an estimate of the molecular volume for each of the seven PEs studied here. These volumes were estimated by assuming that all of the PE polar headgroups have a single invariant volume and that the acyl chain volume may be estimated from known molecular volumes of the "constituent" hydrocarbons, as described above. The hydrocarbons that were used are listed in Table 1 and the estimated lipid molecular volumes are given in Table 2.

18:1c9-PE may be used as an example of the treatment of each of the seven lipids: The volume of 18:1c9-PE is 1190 Å at 25°C (Tate and Gruner, 1989). The methyls on the two hydrocarbon chains occupy a total of 2 × 56 Å³ = 112 Å³, or about 10% of the lipid volume. There are a total of 18 electrons in the methyl groups, yielding an electron density of 0.16 e/ų. The volume of the methylene portion of chains minus the terminal methyls can be estimated by comparison to the known molecular volumes of the constituent hydrocarbons measured at 25°C shown in Table 1,

(2)

From Eq. 2, it is seen that the hydrocarbon chains minus the methyl groups occupy about 70% of the lipid volume and that the remaining 20% is taken up by the headgroup. From the chemical composition of 18:1c9-PE, it is a simple matter to calculate the electron densities for these regions, which are 0.30 e/ų for the hydrocarbon chains and 0.54 e/ų for the polar headgroup. A diagram of this simple model is shown in Fig. 1. The model illustrates the basic features of a correct reconstruction, namely a methyl trough bounded by the headgroup peaks, which give way to the water region, which is of intermediate electron density. Note that this model is appropriate to all of the lipids under study here except for 21:0_ch-PE, which has no terminal methyls. Because there is no methyl trough for 21:0_ch-PE, the electron density in the tail region should be fairly flat.

View larger version (14K): [in this window] [in a new window]   FIGURE 1   Electron density model of the L phase for 18:1c9-PE.

For the L phase, the electron density is given by

(3)

where d is the repeat spacing of the crystal and x is in a direction perpendicular to the membrane surface. The _avg cannot be determined from the reflection data alone, and may be set to zero for the reconstructions on an arbitrary electron density scale.

Inverted hexagonal phase reconstruction

A method of Turner and Gruner (1992) was used to reconstruct the H_II phase. This technique is based on earlier work by Stamatoff and Krimm (1976), who applied it to the lamellar phase. These methods are based on the observation that, if one compares the electron densities of two lamellar phases with slightly different water contents, the correct phasing should yield the electron density that changes the least in going from one hydration to another. This is known as the swelling method of phasing.

Quantitatively, one can define the difference in electron densities as

(4)

where  is a measure of the deviation, A is the area of the unit cell, '_e is the electron density at one hydration, _e is the electron density at another hydration,  is the small difference in the radii of the two water cores, and B and C are constants to take into account differences in absolute and relative scaling, and the integral is performed over the unit cell (Turner and Gruner, 1992). Minimizing  with respect to B and C yields the following formulas for those quantities:

(5)

(6)

For the H_II phase, the electron density is given by

(7)

where

(8)

(9)

For h or k equal to 0 or h = k, the multiplicity for the A_hk is 6. For the remaining cases, the multiplicity is 12.

X-ray diffraction

X-ray diffraction data were acquired as described in Lewis et al. (1989) but with the intensifier/lens/CCD detector described in Tate et al. (1997). Briefly, x-rays were generated on a Rigaku RU-200 rotating anode x-ray generator using a copper anode. The beam was Ni-filtered, point focused via two orthogonal Franks mirrors and the data were recorded on a two-dimensional x-ray detector based on an intensified CCD. Samples consisted of unoriented dispersions of fully hydrated lipid and water, generally in an ~1:1 weight ratio, contained in 1.5 mm glass x-ray capillaries. The x-ray stage was thermostatically controlled to ~0.5°C and a stability of ~0.1°C. Equilibration of the samples was checked by varying the equilibration time between temperature steps until the diffraction was stable when the time was increased. Repeat spacings were calibrated with silver stearate, which has a lamellar repeat of 48.68 Å (Vand et al., 1949).

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS METHODS RESULTS DISCUSSION REFERENCES

Lamellar reconstructions

Diffraction is seen to fourth order for lipids in the L phase. The Lorentz-corrected amplitudes as a function of temperature are listed for each lipid in Table 3. Note that the amplitudes have been normalized to the first-order amplitude and that the multiplicity for each of these peaks is the same.

View this table: [in this window] [in a new window]   TABLE 3   Temperature (T, °C), measured amplitudes, d, w, l, v, and A for several hydrocarbon chain structural variants of diacyl phosphatidylethanolamine in the L phase

Four diffracted orders can have 2⁴ = 16 possible combinations of sign; however, eight of these are simply the negative of the remaining eight combinations (cf. Figs. 2 and 3). Choosing a phasing that is centered on the midplane of the bilayer requires that the middle of the electron density profile be coincident with the terminal methyl dip, thereby eliminating 8 of the 16 possible phase combinations. The remaining combinations are shown in Fig. 2. The minimum must also be bounded by maxima due to the phospholipid headgroups, followed by a decrease in electron density in the water region. The average electron density is set to zero, as noted earlier, and because the electron density of water is about equal to the average electron density of the system, one expects a substantial decrease in the electron density toward zero in the water region. This leaves only + and ++ as viable choices, with a preference toward +, because the dip in the water region is slightly deeper. To resolve this choice satisfactorily, note that it has been shown that 18:1c9-PE has a phasing of + (So et al., 1993). Because 18:1c9-PE is practically identical to 18:1t9-PE in terms of electron density, it seems clear that this is the proper phasing for 18:1t9-PE as well.

View larger version (17K): [in this window] [in a new window]   FIGURE 2   Electron density reconstructions of the L phase for 18:1t9-PE at 55°C. The phasing is shown above the reconstruction. Only phasing combinations in which the first phase is negative are shown in this figure. The y-axis is the electron density in arbitrary units and the x-axis is in angstroms.

View larger version (17K): [in this window] [in a new window]   FIGURE 3   Electron density reconstructions of the L phase for 18:1t9-PE at 55°C. The phasing is shown above the reconstruction. Only phasing combinations in which the first phase is positive are shown in this figure. The y-axis is the electron density in arbitrary units and the x-axis is in angstroms.

For the other lipids studied besides 18:1c9-PE and 18:1t9-PE (except for 21:0_ch-PE), the weak second-order reflection was missing, and so it was straightforward to pick the correct phasing, which was 0+. The correct phasing for 21:0_ch-PE was ++, as shown by the following reasoning. The strong first-order peak must have a minus phasing for the hydrocarbon region to have a lower electron density than the headgroups and the water. A plot of the remaining phase combinations is shown in Fig. 4. The 21:0_ch-PE has no terminal methyls and must therefore have a relatively uniform electron density in the hydrocarbon region. The only phase combination that satisfies this is ++. It is not surprising that most of these lipids have the same phasing because the overall chemical structure of all these lipids is quite similar. Finally, note that these phase choices yield water-layer thicknesses that are the same to within an angstrom for all of the lipids. Because it is reasonable that lipids with the same headgroup and similar hydrocarbon chains should have the same water-layer spacing, this helps confirm these phasing choices.

View larger version (18K): [in this window] [in a new window]   FIGURE 4   Electron density reconstructions of the L phase for 21:0ch-PE at 70°C. The phasing is shown above the reconstruction. The y-axis is the electron density in arbitrary units and the x-axis is in angstroms.

Inverted hexagonal reconstructions

This method was applied to 18:1c9-PE using the amplitudes at 85°C and 95°C. The amplitudes for 18:1c9-PE in the H_II phase are shown in Table 4 and the amplitudes for the other lipids in the H_II phase are shown in Table 5. According to the phasing criteria developed by Turner and Gruner (1992), the best phasing is selected by first eliminating from consideration all phase sets with a scale factor C that varies from 1 by more than 0.05 and then picking the phasing with the lowest  from the remaining choices. The best phasing choice was (+++++) according to the above criteria, with the second-best phase choice having a value of  that was twice as large. This is also the phasing found for the H_II phases of 18:1c9-PE by Turner and Gruner (1992). A reconstruction of 18:1t9-PE using the +++++ phasing is shown in a 3D plot in Fig. 5. The electron density shown is similar to that of 18:1c9-PE (Turner and Gruner, 1992).

View this table: [in this window] [in a new window]   TABLE 4   Temperature (T, °C), measured amplitudes, d, r, l, v, and A for 1,2-di-O-oleoyl-3-O-phosphatidylethanolamine-sn-glycerol in the HII phase

View this table: [in this window] [in a new window]   TABLE 5   Temperature (T, °C), measured amplitudes, d, r, l, v and A for several hydrocarbon chain structural variants of diacyl phosphatidylethanolamine in the HII phase

View larger version (77K): [in this window] [in a new window]   FIGURE 5   A 3D view of the electron density reconstruction of the HII phase for 18:1t9-PE at 85°C.

The phasing +++++ was also found to be the correct phasing for the other PEs studied, using the same phasing method. This is a reasonable result, considering the similarity of the lipids. As will be shown in the following section, several patterns emerge in the structural parameters that also help confirm this phasing choice. For example, the average lipid length appears to decrease by roughly the same amount (1-1.5 Å) across the L/H_II phase transition for all the lipids studied. Additionally, the headgroup areas at the lipid-water interface assume similar values. This physically plausible behavior lends support to the phasing choice.

Structural parameters

The structural parameters of the L and H_II phases are defined in Fig. 6. The dimensions that were found, as described below, are listed in Tables 4-6 and Figs. 6-10. The value of d is readily measured to an accuracy of ±1/2 Å and the position of the lipid-water interface can also be calculated from the electron density reconstruction to a relative accuracy of ±1/2 Å (Turner and Gruner, 1992). Though disorder is certainly present in these systems, the method used to determine the lipid-water interface uses experimental amplitudes that have not been altered to correct for disorder. The values of d are given in Fig. 7, and the values of the water layer thickness (w and r, as defined in Fig. 6) are given in Fig. 8.

View larger version (16K): [in this window] [in a new window]   FIGURE 6   Typical terminology used in this study. (A) The L dimensions, d is the d-spacing, l is the lipid length, and w is the thickness of the water layer between the lipid bilayers. (B) The HII dimensions, d is the d-spacing, lmin is the minimum lipid length, lmax is the maximum lipid length, and r is the water core radius. Note that in both diagrams, A is the headgroup area at the lipid-water interface and S is the area of the hatched region.

View larger version (19K): [in this window] [in a new window]   FIGURE 7   Unit cell lengths (d in Fig. 6) for some hydrocarbon chain structural variants of diacyl phosphatidylethanolamine. Solid lines connect the L data points and dotted lines connect the HII data points. Representative error bars for each phase are plotted for 18:1c9-PE at one data point per phase. , 18:1c9-PE; , 18:1t9-PE; , 20:0eai-PE; , 20:0dmi-PE; , 19:0i-PE; , 19:0ai-PE; , 21:0ch-PE.

View larger version (19K): [in this window] [in a new window]   FIGURE 8   Water layer thickness (w or r in Fig. 6) for some hydrocarbon chain structural variants of diacyl phosphatidylethanolamine. Solid lines connect the L data points and dotted lines connect the HII data points. Representative error bars for each phase are plotted for 18:1c9-PE at one data point per phase. The symbols have the same meaning as in Fig. 7.

The d-spacings for the L and H_II phases formed by the various PEs are presented in Fig. 7. In both phases, they decrease as a function of increasing temperature, although, in general, the rate of decrease is smaller in the L phase than in the H_II phase. The rate of decrease of the d-spacings with temperature in both phases does not depend significantly on chain structure. However, as shown in Table 6, the magnitudes of the d-spacings of the L and H_II phases at temperatures either side of their L/H_II phase transitions do depend significantly on the structure of the hydrocarbon chains. In particular, the d-spacings in the L phase varied from 51.2 to 56.4 Å and those in the H_II phase from 74.9 to 82.7 Å. These results differ from those reported in our earlier study (Lewis et al., 1989), where near-constant d-spacings of 52.5 and 77.0-78.0 Å for the L and H_II phases, respectively, were reported for these PEs. Interestingly, the values of the d-spacings for the 18:1c9- and 18:1t9-PEs are the smallest in both the L and H_II phases, whereas those for 19:0_i and 19:0_ai-PE are intermediate, and those for the 20:0_eai, 20:0_dmi and 21:0_ch-PE are largest. The possible molecular basis for these observations will be discussed in a forthcoming paper to be presented elsewhere (D. A. Mannock, R. N. A. H. Lewis, R. N. McElhaney, P. E. Harper, and S. M. Gruner, submitted for publication).

View this table: [in this window] [in a new window]   TABLE 6   Lipid dimensions (d-spacing, w, r, l and A) at the L/HII phase transition for the hydrocarbon chain structural variants of diacyl phosphatidylethanolamine used in this study

The dependence of the water-layer dimensions for the L and H_II phases formed by the various PEs studied here as a function of temperature are presented in Fig. 8. In general, the thickness of the water layer separating adjoining bilayers in the L phase is much less than the radius of the central water core in the H_II phase, as expected. The L phase water-layer thickness (12.2-13.1 Å) also varies less with changes in the structure of the hydrocarbon chains than does the radius of the water core in the H_II phase, which varies from 20.9 to 23.1 Å (Table 6). Nevertheless, these values vary much less with PE hydrocarbon chain structure than do the d-spacings, indicating that variations in average lipid length and headgroup area at the lipid-water interface must account for most of the observed variations in the bilayer d-spacing. However, the small variations in the radius of the water cylinders in the H_II phase formed by the various PEs follow the same trends as those observed in the d-spacings of the L and H_II phases, suggesting that the structure of the chains also plays a part in determining the monolayer curvature in the H_II phase. With the lipid volumes, V, discussed in the Methods section and a coefficient of expansion of V/V  7 × 10⁴/°C, one can use geometry to calculate the headgroup area at the lipid-water interface. For the L case, the headgroup area is given by

(10)

and, for the H_II case,

(11)

where A is headgroup area at the lipid-water interface, V is the lipid volume, d is d-spacing, and r is the water core radius, all of which are defined in Fig. 6. As expected, the headgroup areas at the lipid-water interface (Fig. 9) are considerably larger and increase more rapidly with increases in temperature in the L phase than in the H_II phase. However, the most important feature of this plot, and the data in Table 6, is that the headgroup areas at the lipid-water interface in both the L and H_II phases just below and just above the L/H_II phase transition are quite similar for each PE hydrocarbon chain variant. These results suggest that the effects emanating from the variation in the structure of hydrocarbon chains on the headgroup area at the lipid-water interface are relatively small.

View larger version (18K): [in this window] [in a new window]   FIGURE 9   Headgroup area at lipid-water interface (A in Fig. 6) for some hydrocarbon chain structural variants of diacyl phosphatidylethanolamine. Solid lines connect the L data points and dotted lines connect the HII data points. Representative error bars for each phase are plotted for 18:1c9-PE at one data point per phase. The symbols have the same meaning as in Fig. 7.

The average lipid lengths are shown in Fig. 10. In calculating the average lipid length for the H_II phase, each length was weighted by the volume of lipid for that length. If one assumes that the volume of each lipid in a given phase at a given temperature is constant, then weighting averages by volume is equivalent to averaging over all the lipids. The derivation for the formula for the average length in the H_II phase is as follows. From Fig. 6, it is noted that l(), the lipid length as a function of  (in radians), is defined

(12)

(13)

From geometry,

(14)

where r is the water core radius, l is lipid length as a function of , and l_min is minimum value of l(), as shown in Fig. 6. Define

(15)

for computational convenience. Solving for l yields

(16)

(17)

For the area S, as in Fig. 6,

(18)

(19)

(20)

Finally, l, the average lipid length, is given by

(21)

(22)

which to first order in (  1), is

(23)

Note that the expansion for l is accurate to ±0.2% for 0.5 <  < 1.5. 

View larger version (20K): [in this window] [in a new window]   FIGURE 10   Average lipid length (l in Fig. 6) for some hydrocarbon chain structural variants of diacyl phosphatidylethanolamine. Solid lines connect the L data points and dotted lines connect the HII data points. Representative error bars for each phase are plotted for 18:1c9-PE at one data point per phase. The symbols have the same meaning as in Fig. 7.

The dependence of lipid length on temperature in the L and H_II phases formed by the various PEs studied here is presented in Fig. 10. In all cases, the lipid lengths decrease with increasing temperature in both phases at roughly comparable rates with an abrupt decrease of 1.5-2.0 Å at the L/H_II phase transition, as expected (Table 6). The magnitude of the lipid length values also changes with hydrocarbon chain structure as was observed with the d-spacings. Typically, the lipid lengths in both the L and H_II phases of the 18:1c9- and 18:1t9-PEs are smallest, those for 19:0_i and 19:0_ai-PE are intermediate, and those for the 20:0_eai, 20:0_dmi, and 21:0_ch-PE are the largest. Thus, the bulk and position of the substituent branch on the hydrocarbon chain determine T_h by moderating the ability of the hydrocarbon chains to shorten as a function of increasing temperature. Once again, the possible molecular basis for these observations will be discussed in a forthcoming paper to be presented elsewhere (D. A. Mannock, R. N. A. H. Lewis, R. N. McElhaney, P. E. Harper, and S. M. Gruner, submitted for publication).

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS METHODS RESULTS DISCUSSION REFERENCES

The original impetus for this study came from an observation that, at the L/H_II phase transition, all of these PEs had very similar L and H_II d-spacings (Lewis et al., 1989). The goal of this study was to check whether the internal dimensions followed the same pattern. In fact, it turns out that the dimensions, both internal and external, vary by over 10%. The difference with our earlier measurements (Lewis et al., 1989) has been traced to faulty temperature calibration. This result underscores the need for accurate temperature calibrations.

Besides correcting the earlier study, there are a number of interesting features of the data that add insight into PE phase behavior. The first is that the water-layer thickness in the L phase is the same to within one angstrom for all of these PEs (Fig. 8). This suggests that the headgroup plays the dominant role in setting the interlamellar water-layer thickness, with the hydrocarbon chains playing a secondary role. It is also interesting to note that the water layer shrinks at roughly the same rate as the increase of the headgroup area at the lipid-water interface, implying that the property of the headgroups that sets the water-layer spacing varies inversely with the headgroup area.

The rate of contraction of the hydrocarbon chains with increasing temperature for a given lipid is roughly the same in both the L and H_II phases. There is also a small decrease in l of ~1.0-2.0 Å across the phase transition, an amount that is approximately the same for all the PEs under study (Fig. 10). The behavior of the headgroup area at the lipid-water interface is far more dramatic, as the headgroup area increases in the L phase, and then drops dramatically across the L/H_II phase transition. The headgroup areas at the lipid-water interface also tend to have similar values in the H_II phase (Fig. 9) regardless of the hydrocarbon chain structure.

Comparison of the headgroup area at the lipid-water interface in these PEs shows that the values of A are considerably larger and increase more rapidly with an increase in temperature in the L phase than in the H_II phase. However, at temperatures just below and just above the T_h, the values of A in both the L phase and the H_II phase are largely independent of hydrocarbon chain structure. These results indicate that, although differences in hydrocarbon chain structure may determine the T_h on the absolute temperature scale by virtue of differences in the rate of hydrocarbon chain shortening, the structure of the hydrocarbon chains probably makes only a small contribution to the limiting area per molecule at the lipid-water interface in both the L and H_II phases of these PEs. An overview of the l and A data suggests that these two parameters are in direct competition, with the decreasing lipid length driving the lipid-water interface to larger and larger areas in the L phase. Eventually, the lamellar morphology becomes too costly energetically, and the system is forced to adopt the H_II phase, where the extra degree of geometric freedom allows both the hydrocarbon chains and polar headgroups to assume their desired states.

The following picture is suggested as an explanation for this behavior (Tate and Gruner, 1989). There are two main free energies in the system, one driving the hydrocarbon chains to a desired length that decreases with increasing temperature and the other free energy pushing the headgroup to an optimum area that is relatively temperature independent. In the L phase (for a nearly constant molecular volume), the lipid length and headgroup area at the lipid-water interface are uniquely related (see Eq. 10). Hence, these two free energies are in direct competition, with the decreasing lipid length and concomitant splaying of the hydrocarbon chains driving the lipid-water interface to larger and larger areas. Eventually, this becomes too costly and the system is forced into the H_II phase, where the extra degree of geometric freedom allows both the hydrocarbon chains and headgroups to assume (on average) their desired states. The only free energy cost keeping the system out of the H_II phase is that the lipid hydrocarbon chains are forced to assume a variety of lengths to fill the hexagon (see Fig. 6). This free energy cost due to the packing of the lipid chains in the H_II phase was demonstrated by Kirk et al. (1984).

These observations will be extended in another paper to be presented elsewhere by considering lipids with a similar spectrum of hydrocarbon chain structures but different chain lengths and polar headgroups (D. A. Mannock, R. N. A. H. Lewis, R. N. McElhaney, P. E. Harper, and S. M. Gruner, submitted for publication).