Fluid bilayer structure determination by the combined use of x-ray and neutron diffraction. II. "Composition-space" refinement method

Abstract

This is the second of two papers describing a method for the joint refinement of the structure of fluid bilayers using x-ray and neutron diffraction data. We showed in the first paper (Wiener, M. C., and S. H. White. 1990. Biophys. J. 59:162-173) that fluid bilayers generally consist of a nearly perfect lattice of thermally disordered unit cells and that the canonical resolution d/hmax is a measure of the widths of quasimolecular components represented by simple Gaussian functions. The thermal disorder makes possible a "composition space" representation in which the quasimolecular Gaussian distributions describe the number or probability of occupancy per unit length across the width of the bilayer of each component. This representation permits the joint refinement of neutron and x-ray lamellar diffraction data by means of a single quasimolecular structure that is fit simultaneously to both diffraction data sets. Scaling of each component by the appropriate neutron or x-ray scattering length maps the composition space profile to the appropriate scattering length space for comparison to experimental data. Other extensive properties, such as mass, can also be obtained by an appropriate scaling of the refined composition space structure. Based upon simple bilayer models involving crystal and liquid crystal structural information, we estimate that a fluid bilayer with hmax observed diffraction orders will be accurately represented by a structure with approximately hmax quasimolecular components. Strategies for assignment of quasimolecular components are demonstrated through detailed parsing of a phospholipid molecule based upon the one-dimensional projection of the crystal structure of dimyristoylphosphatidylcholine. Finally, we discuss in detail the number of experimental variables required for the composition space joint refinement. We find fluid bilayer structures to be marginally determined by the experimental data. The analysis of errors, which takes on particular importance under these circumstances, is also discussed.

Continuous distribution model for the investigation of complex molecular architectures near interfaces with scattering techniques

“…These approaches were refined to parameterize molecular components and their configurations within a sample, an approach termed composition-space refinement. 10,11 In reflectometry, even if scattering length density (SLD) profiles can be worked out from first principles or can be determined by direct inversion, 15,16 composition-space refinement has advantages in that it allows intuitive models to be implemented that constrain the full range of SLD profiles by retaining only those relevant for plausible chemical structures. This is particularly important in neutron scattering when using isotopic variation of selected chemical species, typically by 1 H= 2 H substitution in biological samples.…”

“…Finally, this approach also permits the consistent evaluation of x-ray and neutron measurements of identically prepared samples. 10,11 In more detail, a composition-space refinement approach for NR represents sub-molecular components of the sample as cross-sectional area profiles A(z) along an axis of orientation z, which for membrane studies usually is the bilayer normal. Figure 1 shows the space-filling structures of two molecules of a membrane-forming lipid, DMPC, 17 arranged in opposite leaflets of a bilayer and the out-of-plane distributions of its sub-molecular components as obtained from a molecular dynamics (MD) simulation.…”

“…[7][8][9] Here we describe a flexible and modular modeling technique, based on earlier work in our lab and others, [10][11][12][13] to maximize the information extracted from reflectivity measurements of substrate-supported bilayers. While simple slab models ("box" models) 11 are still widely used in the evaluation of reflectometry data of membrane structures, such models cannot describe partial overlap of molecular fragments along the membrane normal.…”

Direct Comparison of Disaccharide Interaction with Lipid Membranes at Reduced Hydrations

“…Small angle neutron scattering has shown that sugars partition unequally between lipid phases and coexisting excess solution phases, giving a mesoscopic view of the sugar location within lipid bilayer systems 23 . Recently 37 we have demonstrated how the membrane neutron diffraction technique [38][39][40][41][42] can be used to directly extract the density profile of sugar molecules in the aqueous layer between opposing lipid bilayers. It was shown, at a single sugar composition, that the density profile is a Gaussian centered in the water layer.…”

“…It was shown, at a single sugar composition, that the density profile is a Gaussian centered in the water layer. This approach 41 , where the components of a fluid bilayer are decomposed into quasi-molecular fragments, and a Gaussian describes the probability of occupancy per unit length across the bilayer (Figure 1), was extended to extract the profile of the sugar molecules. As lipid bilayer membranes are forced into close proximity due to dehydration, they form stacks of bilayers periodically interspersed with aqueous solution.…”