Electron diffraction from phospholipids - an approximate correction for dynamical scattering and tests for a correct phase determination

An approximate experimental correction of electron diffraction intensities from an epitaxically crystallized phospholipid bilayer for dynamical scattering is described. This correction, which is useful for certain low-angle centrosymmetric data sets, compares intensities recorded at high and low electron-accelerating voltages to ascertain which reflections are most affected by n-beam interactions. When applied to experimental intensity data from 1,2-dihexadecyl-sn-glycerophosphoethanolamine (DHPE), the correction facilitates a direct phase determination based on the probabilistic estimate of three-phase invariants because a more accurate estimate of the hierarchy of |E_l| values is obtained. When a multisolution technique is used, incorporating algebraic unknowns for certain phase values, the best phase assignment can be assessed by comparison of the single convolution of phased structure factors to the observed structure-factor magnitudes for the low-voltage data. This approach exploits an approximate analogy made earlier by Moodie between the Sayre equation and the phase grating series and is valid as long as the single convolution adequately models experimental low-voltage data (a condition favored by light-atom structures in a low-angle region of reciprocal space). In real space, the correct structure can also be readily identified as the one having the smoothest density profile.