DISCUSSION

Our primary experimental results are the ratios of form factors reported in Table I for various levels of hydration. These data provide a basic test for theoretical models of phase DPPC bilayers, such as those obtained from computer simulations, much like the traditional NMR order parameters (Seelig, 1977) that are most frequently employed as a test. To perform this test electron density profiles obtained by theory should be Fourier transformed to obtain .

The particular innovation used in this study to obtain the is the combined use of x-ray scattering at very high instrumental resolution and the modified Caillé peak shape theory (Zhang et al., 1994) to obtain the true scattering intensity under the entire peak, including the long power law tails predicted by this theory and verified experimentally (Roux and Safinya, 1988; Zhang et al., 1995b). This analysis obtains the Caillé fluctuation parameter which is shown in Fig. 2 and which decreases as D-spacing decreases. From the definition of following Eq. 1, this suggests that the compression modulus B increases with dehydration and that the interactions between bilayers become stronger as the water space decreases. Further analysis of the forces involved will be deferred to another paper. Most importantly for this paper, this analysis of the experimental data is essential to obtain the correct continuous scattering transform F(q) and to explain why some of the higher order peaks for the more hydrated samples can not be seen.

Our F(q) transform in Fig. 4 is consistent with no change in bilayer structure for the phase of DPPC as the bilayer is dehydrated from a D-spacing of 67.2Å to 53.9Å. As is shown by Fig. 5, this conclusion can not be drawn if one performs a straightforward integration of the central peak intensities that ignores the long power law tails. Even the form factors for the h=2 order are systematically too small with higher hydration, and some of the h=3 orders should have been seen, but could not be. However, we now know that this is due to the loss of intensity into the tails, which is impossible to separate from background without an appropriate theory to perform the extrapolation from the measured peak shapes. This in turn requires high resolution x-ray detection that was achieved with our experimental configuration at CHESS.

We conclude from our data that the threshold spacing , above which the bilayer structure effectively does not change, must be smaller than 54Å. This conclusion is supported by the results of Torbet and Wilkins (1976) for the gel phase of DPPC which showed that fairly small changes in bilayer thickness resulted in rather large changes in the continuous transform. This conclusion disagrees with conclusions drawn from x-ray studies using the gravimetric method of Luzzati which indicated that bilayer structure changed continuously as the system is dehydrated from full hydration (Tardieu et al., 1973; Lis et al., 1982). The latter conclusion had implied that results from studies on partially dehydrated samples, such as the classic neutron diffraction studies on specifically deuterated lipids (Buldt et al., 1979; Zaccai et al., 1979) where the D-spacing was 54.1Å, are biologically less relevant. One likely source of error in the gravimetric method is the assumption that all the water resides neatly between the bilayers (Wiener et al., 1989; Klose et al., 1988). This is quite unlikely for multilamellar vesicles that must have extra water in small volumes in the center of each MLV as well as in regions between different MLVs. Only in well-oriented planar arrays could one hope that this assumption is valid. Also, the areas A from gravimetric studies have been consistently larger than those obtained by other methods; this discrepancy is also explained by the assumption about water residence being incorrect. In the case of gel phase DPPC, we have shown previously for both oriented (Tristram-Nagle et al., 1993) and powder, multilamellar vesicular samples (Sun et al., 1994), that the gravimetric method gave erroneously large results for A. Although our present results do not go to low enough hydration to find the value of the dehydration threshold , they do require that be smaller than 54Å and this suffices to validate the biological relevance of the neutron diffraction results for phase DPPC at as well as to provide support for x-ray studies that attempt to obtain membrane structure for partially dehydrated samples.

On the other hand, since one would expect that dehydration would alter the forces between bilayers and that this could change their structure, it is worth discussing quantitatively how much dehydration was required to obtain samples with D=54Å. In Table II it is shown that only a little less than half the water must be removed, leaving waters even when . This is even more water than resides in the fully hydrated gel phase. Also, the mean pure water spacing Å between headgroups is still large enough to avoid much direct contact between headgroups on adjacent bilayers because, as shown by Zhang et al. (1995b), the mean fluctuation in adjacent bilayer spacing is only about Å for the value of that is obtained for D = 54Å from Fig. 2. Furthermore, the relative humidity for our most dehydrated samples is still about 98%. In addition, we have performed differential scanning calorimetry on this sample and find that the main transition temperature rises at most ; this is much less than the rise in for fully dehydrated samples which exceeds . Finally, the work W done against the hydration force is given by the product of the osmotic pressure of our most dehydrated sample (), the area and the decay length , which is given as 1.7Å for egg lecithin (McIntosh and Simon, 1986a); this yields 0.03 kcal/mol, which is considerably less than the enthalpy 8.7kcal/mol for the main phase transition which sets the scale for major structural changes. Therefore, our experimental result that bilayer structure does not change measurably upon dehydrating to D=54Å is theoretically plausible and consistent with our determination of structure reported in Table II.

It may also be noted that the threshold hypothesis implies that there is unlikely to be any structural difference between bilayers in large unilamellar vesicles and those in multilamellar vesicles. This follows because the inter-bilayer interactions become considerably stronger upon dehydration. If these increasingly stronger interactions do not change the bilayer structure, then the weaker interbilayer forces present in fully hydrated multilamellar vesicles would not change the bilayer structure compared to isolated large unilamellar vesicles.

Electron density profiles have been obtained in two ways. The first and most straightforward way that has been employed by many previous workers is to plot the Fourier series using the maximum number of orders of diffraction, which for our data is . Earlier use of this procedure has also indicated that the thickness of bilayers does not change upon dehydrating with PVP for either the gel phase of DPPC or the phase of egg lecithin (McIntosh, 1986a). One of our concerns with this earlier conclusion was that fluctuation corrections were not made and that this would be expected to distort the form factors as shown in Fig. 5 compared to Fig. 4. However, our result in Fig. 6 and our theory in the Appendix shows that fluctuation corrections have almost no effect upon the apparent head-head spacing and this was the major result required by the earlier work. Since only the widths of the peaks and the methyl troughs are affected, our results therefore support the methodology of the earlier work as well as the conclusion that there is little change in bilayer structure upon mild dehydration.

A major goal that we believe we have achieved is to obtain the area for phase DPPC at 50C, which is the most commonly compared temperature. Although does not depend upon hydration down to the threshold, it is expected to depend fairly strongly on temperature, especially near the main transition (Zhang et al., 1995a), as well as exhibiting a gradual increase with increasing T above 50C, but we have not included these effects in this study. Our primary method was adapted from one introduced by McIntosh and Simon (1986b) that obtains for the phase from Eq. 7 which uses gel phase quantities (Tristram-Nagle et al., 1993; Sun et al., 1994), measured volume changes (Nagle and Wiener, 1988) and the changes in the head-head positions, , which are obtained in this paper. The Fourier method works quite well, yielding Å and Å, despite having only three samples with orders.

We have also used a method of analysis that treats all the data with different D-spacings globally. This method requires a model electron density function. We have used the hybrid model proposed earlier (Nagle and Wiener, 1989) after showing in Fig. 7 that it adequately represents the electron density profiles of current molecular dynamics simulations, which also agree with the main assumption that the methylene density is effectively constant in the hydrocarbon region as shown in Fig. 8. There are three constraints on the electron density profile (Nagle and Wiener, 1989) that have been employed to yield the various experimental electron density profiles as shown in Fig. 9. Our methodology for calculating area using Eq. 8 then yields Å.

The values of in the experimental electron density profiles in Fig. 9 are in excellent agreement with the recent simulation of Tu et al. (1995), also shown in Fig. 9, which has Å. One discrepancy that arises is that use of this value of in Eq. 7 yields Å which is larger than Å obtained from the simulation. However, the same spatial resolution and methodology should be used for both the gel and the fluid phases in calculating the difference in , so that we should use the value Å obtained from a 1G fit to the simulated electron density profile (see Fig. 7). This yields Å from Eq. 7 which is satisfactorily close to Å and supports our methodology for obtaining . Another minor inconsistency arises from applying Eq. 8 to our 1G fit to the simulated methyl trough of Tu et al. (1995). This yields Å assuming that and that Å; the latter value appears consistent with the simulated curve in Fig. 9 and also emerges from our 1G fit to these data. However, the plateau level for the number density in Fig. 8 gives closer to Å. Using this latter value of changes the size of the methyl trough so that then yields 62Å using Eq. 8. While this removes the inconsistency, it warns one that, despite the good fit of the 1G model to the simulated data, the parameters for that emerge from the fit seem to be corrupted by mixing with other parameters so that Eq. 8 does not give accurate values for . Another discrepancy is that our hybrid model headgroup peaks are much higher than the simulated headgroup peaks in Fig. 9. In this latter regard, our best hybrid model result shown by the solid line in Fig. 9 agrees better with the simulations of Feller et al. (1995) shown in Fig. 7, even though these simulations were performed at a larger constant area of Å and consequently have a smaller Å when fitted to a 1G model.

The most surprising result in Fig. 9 is the relative narrowness of our headgroup peaks and the methyl trough. The 1G methyl trough for our fully constrained fit has a half-width (Å), not much wider than the 1G methyl trough for the gel phase (Å) and narrower than the Gaussian fit to the simulation methyl trough (Å). The 1G headgroups have half-widths (Å) which are narrower than the gel phase results (Å) and the fluid phase simulations (Å). It is possible that the narrowness of our model electron density profiles is related to intrinsic errors in analytically continuing the F(q) curve to high q. Although the lack of data at higher angles always broadens features in Fourier reconstructions of the electron density profile, this is not necessarily the case for the model method, as we have confirmed by taking a known model electron density profile, Fourier analyzing it, adding noise to the Fouriers, fitting models to the Fouriers, and then comparing to the original model electron density. Finally, when we did a fit with all three constraints, but with fixed to 0.304e/Å, the methyl trough half-width increased substantially to Å. In contrast, only increased by 0.1Å, so widths of features in the hybrid model may be less certain than the head-head spacing, which is the crucial quantity for obtaining the area .

Our main result that bilayer structure does not change with mild dehydration down to 54Å allows us to use the older neutron diffraction results, which were obtained for Å, in two new ways to obtain additional estimates, Å and Å, for . For our final estimate of , we averaged these with two x-ray results, Å from Fourier analysis and Å from hybrid modeling to obtain our final diffraction result, Å in the phase of DPPC at 50C.

The other major way of determining uses the NMR order parameters. Although the NMR method has been employed in several different ways giving considerably different values of , our recent analysis gave Å for DPPC under the same conditions as in this paper (Nagle, 1993), in good agreement with the present diffraction result. Even the sign of the small difference can be understood because the NMR result assumed no backtracking of chains, which, if present, would increase the NMR estimate of . As more quantitative information about backtracking becomes available from simulations, quantitative changes in the NMR estimate can be made.

Our value of is smaller than the value Å determined for unilamellar vesicles by Lewis and Engelman (1983) using weak continuous scattering. It is considerably smaller than the Å obtained by the gravimetric method (Lis et al., 1982) or the Å obtained by modifying that method (Rand and Parsegian, 1989) to try to account for inconsistency with lateral compressibility data. This latter value of was assumed in the simulations of Feller et al. (1995). A recent simulation (Essmann et al., 1995) used a fixed value Å for nearly fully hydrated DPPC with . Other recent simulations employ constant pressure ensembles rather than constant area ensembles and this allows for the simulation to determine the best . Chiu et al. (1995) obtain the rather smaller Å at 52C, but this was for DMPC. The recent simulations for DPPC by Tu et al. (1995) yield Å, in excellent agreement with our values for .

The variety of simulation results for ostensibly the same lipid bilayer emphasizes that there are many non-canonical choices to be made when doing a simulation. It is clearly important that critical experimental data be available to test choices in potentials, effect of initial configuration (since effective running times are only nsec, during which the system may hang in a metastable state), and choice of ensemble parameters such as effective lateral pressure. In this regard, we emphasize that the ratios of form factors in Table I should be compared to simulations. (Direct comparison to our primary data, the scattering peaks, would require simulations on bilayers of square micron size, which is rather unlikely to be feasible.) However, we emphasize that simulation results, even if all the simulation choices are not perfect and even if all the simulations do not agree, are extremely valuable in testing assumptions used in analyzing data, as we show in Figs. 7 and 8 in this paper and as was previously mentioned in the analysis of NMR data (Nagle, 1993).

Fluid phase lipid bilayers are difficult to study experimentally, due to their partially ordered/disordered nature which gives rise to non-trivial fluctuations. We believe the present study has made substantial progress on this point. We anticipate that combined experimental and simulation studies will resolve remaining issues and provide a methodological foundation for quantitatively comparing bilayers composed of different lipids.

Acknowledgments: For providing the results of molecular dynamics simulations shown in Figures 7 and 8, we thank the members of three simulation groups, particularly Scott Feller, Richard Venable and Richard Pastor; Larry Scott; Michael Klein, Doug Tobias and especially Kechuan Tu for visits to our laboratory and extensive interaction. We thank our CHESS collaborators R. L. Headrick and T. C. Irving for their help in acquiring the basic scattering data. Synchrotron beam time was provided under CHESS proposal P619. This research was supported by NIH Grant No. GM44976.