Direct phase determination in protein electron crystallography: The pseudo-atom approximation

Abstract

The crystal structure of halorhodopsin is determined directly in its centrosymmetric projection using 6.0-Å-resolution electron diffraction intensities, without including any previous phase information from the Fourier transform of electron micrographs. The potential distribution in the projection is assumed a priori to be an assembly of globular densities. By an appropriate dimensional re-scaling, these ''globs'' are then assumed to be pseudo-atoms for normalization of the observed structure factors. After this treatment, the structure is determined directly by conventional direct methods, followed by Fourier refinement, leading to a mean phase deviation of only 20؇ (from the values originally found from the image transform) for the 45 most intense ref lections.

Direct structure analysis in protein electron crystallography via the density histogram: deoxycholate-treated purple membrane

“…Since the normalization of diffracted intensity from macromolecules is, at low resolution, most accurately based on the transform of these globular subunits (Harker, 1953) than on the aggregate of individual atoms in the molecule, the rationale for this approximation becomes clear. The approximate validity of the globic approximation for these helical proteins, via an atomic scattering factor and dimensional re-scaling, has been further demonstrated by the fit of the low resolution intensity data by a Wilson plot (Dorset, 1997a). It is also evident that, to a certain extent, Fourier refinement can also be used in a way similar to its application to small molecule problems.…”

“…As shown elsewhere (Dorset, 1997a), because a-helices in fibrous proteins will pack with a center to center distance of about 15 A, the 1.54 A distance of a carbon-carbon single bond suggests that a 10-fold scale reduction of the structural problem may permit the Fourier transform of a glob to be simulated by, say, a carbon scattering factor (or any similar Gaussian or Lorentzian shape). (In terms of the above dimensions, re-scaling causes the unit cell length to be 5.73 A and the data resolution to be 0.62 A.)…”

“…In electron crystallography, ab initio determinations have been quite successful for centrosymmetric projections of proteins where a globular approximation to density distribution is valid (Dorset, 1997a(Dorset, , 1998Dorset, Jap, 1998;Dorset, Gilmore, 1999). Analysis of such zones by maximum entropy and likelihood has also be quite successful (Gilmore, Nicholson, Dorset, 1996;Gilmore, 1999).…”

Nanocrystals: Solving Crystal Structures Using Electron Crystallography

“…In particular the macromolecule does not consist of atoms but of 'globs' of density which can be used as pseudo-atoms. This reduces the complexity of the problem by at least one order of magnitude (Dorset, 1997), by reducing N in the concentration factor for triplets in Eq. (2.2).…”

Putting structure into context: fitting of atomic models into electron microscopic and electron tomographic reconstructions

“…The resulting models are often referred to as 'pseudo-atomic' models to hint at the fact that the accuracy of the atom positioning is of limited resolution. This is an unfortunate and confusing term because the models are built out of actual atoms and the term ‘pseudo atom’ is often used to denote atom-like representations of entire residues or other groups of atoms in coarse-grained molecular modeling [28], direct phasing approaches [29,30] or nuclear magnetic resonance calculations [31]. …”