Fluid Bilayer Structure Determination by the Combined Use of X-ray and Neutron Diffraction. I. Fluid Bilayer Models and the Limits of Resolution

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.