Fluid bilayer structure determination by the combined use of x-ray and neutron diffraction. I. Fluid bilayer models and the limits of resolution

Abstract

This is the first in a series of papers concerned with methods for the determination of the structures of fluid phospholipid bilayers in the liquid-crystalline (L alpha) phase. The basic approach is the joint refinement of quasimolecular models (King and White, 1986. Biophys. J. 49:1047-1054) using x-ray and neutron diffraction data. We present here (a) the rationale for quasimolecular models, (b) the nature of the resolution problem for thermally disordered bilayers, and (c) an analysis of the resolution of experiments in which Gaussian functions are used to describe the distribution of submolecular components. We show that multilamellar liquid-crystalline bilayers are best described by the convolution of a perfect lattice function with a thermally disordered bilayer unit cell. Lamellar diffraction measurements on such a system generally yield only 5-10 orders of diffraction data from which transbilayer profiles of the unit cell can be constructed. The canonical resolution of these transbilayer profiles, defined as the Bragg spacing divided by the index of the highest recorded diffraction order, is typically 5-10 A. Using simple model calculations, we show that the canonical resolution is a measure of the widths of the distributions of constituents of the unit cell rather than a measure of the spatial separation of the distributions. The widths provide a measure of the thermal motion of the bilayer constituents which can be described by Gaussian functions. The equilibrium positions of the centers of the distributions can be determined with a precision of 0.1-0.5 A based upon typical experimental errors.

Energetics of stalk intermediates in membrane fusion are controlled by lipid composition

“…3A displays 2D electron density maps normalized to max Δρð~rÞ ¼ 1 for slices through single stalks. In contrast to conventional crystallography, lipidic structures lack fixed atomic positions and are characterized by thermal disorder and fluctuations (44). Therefore, they are represented by smooth continuous electron density distributions with limited resolution compared to e.g., protein crystallography.…”

Stalk structures in lipid bilayer fusion studied by x-ray diffraction

“…Therefore, it is important to consider if observed small changes correctly reflect reality, or possibly are artifacts due to poor resolution. This section summarizes some considerations made by WHITE et al [100,121] and NAGLE et al [47] for the case of bilayer stacks. They should apply to the stalk phase as well.…”

“…For a perfect crystal with fixed atomic positions, it is possible to write F ( q ) as a sum over the scattering amplitudes of the single atoms inside the unit cell using the so-called atomic form factors. As discussed in detail in section 2.6, phospholipid mesophases are characterized by long-range lattice symmetry, but highly disordered unit cells [100]. Therefore, a continuous unit cell electron density distribution ρ u.c.…”

Hydration of POPC bilayers studied by 1H-PFG-MAS-NOESY and neutron diffraction

“…Sample thickness was reduced and the proper corrections applied to eliminate an influence from extinction on data analysis (Bacon and Lowde 1948); (Worcester et al, unpublished). The magnitude of structure factors decreases somewhat with increasing hydration due to increases in bilayer disorder (Hristova 1998;Wiener and White 1991a). …”