Method for Determining A from

One of our main goals has been to obtain the area A per lipid molecule at the water/bilayer interface. Since this involves information about the structure in the direction along the surface of the bilayer, whereas low angle scattering involves information along the direction of the bilayer normal, other information must be used. We will adapt a method introduced by McIntosh and Simon (1986b) and applied by them to DLPE. This method makes use of the well-determined gel phase quantities and of measured differences with the phase. The quantities involved are area A, lipid volume , hydrocarbon chain thickness which is half the thickness of the hydrocarbon region in a bilayer, and head-head spacing ; superscript G will designate gel phase and superscript F will designate fluid () phase quantities. The method begins with the statement that the change in volume takes place only in the hydrocarbon region, so

The justification for assuming that there is little change in volume of the headgroup region is that water can freely enter this region and fill any volume that is voided by the headgroups in going from the gel to the fluid phase (see Wiener et al. (1988) or Nagle and Wilkinson (1978) for more discussion of this assumption). We next write

which assumes that the major determinant of changes in is changes in the hydrocarbon region. Even though the headgroups might be expected to adopt a different mixture of conformations in the two phases, the lever arm for distance changes due to headgroup changes is short, essentially from the carbonyls to the phosphate since the choline is not electron dense, so that Eq. 6 should be a reasonable first approximation. It may be noted, however, that the assumptions behind both Eq. 5 and Eq. 6 should be subject to testing and possible modification by molecular dynamics simulations. Solving Eqs. 5 and 6 yields

To apply Eq. 7 we use volume measurements summarized by Nagle and Wiener (1988) which gave =1232Å at 50C and Å at 20C. Our best wide angle x-ray determination of the gel phase (Sun et al., 1994) gives =47.9 and =17.23 (corrected from to ). Using the values =44.2Å and =39.6Å obtained from Fig. 6 and the preceding subsection and using Eq. 7 then gives = 61.2Å.