Diffuse X-ray Scattering Provides More and Better Information About Membranes than Traditional Diffraction Methods
John F. Nagle
Departments of Physics and Biological Sciences
Carnegie Mellon University
Pittsburgh, Pennsylvania 15213
My group has been developing a new method to obtain structure of lipid bilayers. The new structural method is revolutionary when compared to the conventional crystallographic method that focuses on Bragg peaks from the lamellar diffraction orders. The method also obtains the material parameters for these smectic liquid crystal samples.
The conventional method fails for the most biologically relevant, fluid, liquid-crystalline samples because liquid crystalline fluctuations of the second kind smear out the higher order diffraction peaks. In our work in the 1990s (we think of this as our first revolutionary method that is summarized in BBA 1469 (2000) 159-195) we fought the fluctuations by using smectic liquid crystal theory to re-capture the intensity in the peaks and then we used conventional crystallographic analysis of the recovered peak intensities. While we obtained many results that our new method is confirming, we could not obtain more than four orders of diffraction, and even this required reducing the relative humidity to 97% and that removed half the total water and most of the free water between adjacent bilayers.
We now realize that it is better to exploit the fluctuations than to fight them. The fluctuations produce copious diffuse scattering that contains much more information than is in the conventional Bragg peaks. Although much weaker than peak scattering, diffuse scattering intensity is easily measured using CCDs with synchrotron sources. By using oriented samples and first analyzing the data in the q r direction perpendicular to the direction defined by the line of Bragg peaks, we evaluate the material parameters consisting of the bending modulus K C and the compression modulus B that determine the smectic liquid crystal free energy. The fit to over 500 sets of data in the q r direction, each with over 200 intensities and with only one scaling factor and one background constant, is excellent for DOPC and almost as good for DMPC. This validates our use of the smectic theory to analyze the diffuse intensity to obtain the lipid bilayer form factor F(q). This is even more attractive now because, instead of a maximum of four values of F(q) for each hydration level given by the conventional method, the new method provides over 500 values of F(q) just from one fully hydrated sample.
Our analysis that obtains electron density profiles from the continuous transforms enables us to bring in other measurements, such as our lipid volume, and insights from molecular dynamics simulations, such as the ratio of the electron density peaks of the phosphate and carbonyl groups. Our analysis obtains the thickness of the hydrophobic hydrocarbon chain region, of importance for protein insertion, and area/lipid A, of importance for testing and guiding MD simulations. This analysis obtains absolute electron densities.
Results have now been published for DOPC at T=30C (Liu and Nagle, Phys Rev E 69 (2004) 040901) and many additional details are available in Liu’s thesis posted on http://lipid.phys.cmu.edu. New results for DMPC have also been obtained. The results for DOPC were compared to an earlier simulation of Scott Feller in Rich Pastor’s lab that was performed with the area A that we had obtained with our older method (BBA 2000); that area did not change in our new analysis. The agreement of the simulation and our new profile is outstanding for the shape and position of the headgroup electron densities and the absolute electron density scale. (A figure is included in Chem Phys Lipids 127 (2004) 3-14). This agreement suggests that the wealth of detailed information available from the DOPC simulation regarding detailed distributions of chemical components of the lipid and the water is reliable.
This research is supported by the National Institutes of Health through Grant GM44976.
