Determination of lattice-transform density profiles for multilayered three-dimensional microcrystals in electron crystallography

Abstract

Electron crystallography on multilayered three-dimensional microcrystals has been limited in application by the need to de®ne precisely the three-dimensional shape of the diffraction density pro®les. A new method is presented here to obtain this pro®le from experimental spot positions which are shifted in a characteristic way from the expected Bragg positions. While the Bragg positions are de®ned by the diffraction geometry, the characteristic shift additionally depends on the density pro®le in Fourier space. In general, these two effects are intermingled. A new correlation approach is presented which uses characteristic shift patterns to separate these effects. This technique also allows the determination of all three crystallographic unit-cell dimensions from a single tilted electron diffraction pattern. It was tested on simulated diffraction patterns and applied to experimental data of frozen hydrated crystals of the protein catalase. Since multilayered catalase crystals with different numbers of crystallographic layers were studied, an inhomogeneous data set had to be evaluated. Processing of such data is now possible using the new correlation approach.

Global least-squares determination of Eulerian angles from single electron diffraction patterns of tilted crystals

“…In experiments with thin three-dimensional microcrystals consisting of only a few layers in the z direction, additional effects have to be taken into account. Diffraction patterns of three-dimensional microcrystals show a characteristic shift of the spot positions resulting from the special shape of the reciprocal lattice (for details see Dimmeler et al, 2000). If a Gaussian density pro®le is intersected non-centrally by a nearly¯at Ewald sphere, the projected spot on the recording plane is shifted relative to the position where the spot of a rodshaped reciprocal lattice would be located.…”

“…A data set of a three-dimensional crystal can, for the ®rst time, be analysed without using the molecular transform for successive re®nement steps by the use of the new tilt angle determination method. In a separate procedure, the three-dimensional pro®le of the diffraction density in reciprocal space can be determined (Dimmeler et al, 2000). The combination of the two methods would allow the processing of diffraction patterns with not perfectly intersecting crystallographic zones (see Figs.…”

“…Therefore these parameters should be found independently of the determination of tilt angles. A new method for determining the shape of the lattice transform has been presented by Dimmeler et al (2000). The success of electron crystallography with any given three-dimensional crystals depends crucially on the accurate determination of the tilt angles in a diffraction pattern.…”

Design guidelines for an electron diffractometer for structural chemistry and structural biology

“…The size of single crystals for routine structure determination is limited to a side length of about 5-10 mm when X-rays are used as a radiation source. With electron radiation, no such size limit exists (Dimmeler et al, 2000). Experiments in 3D electron crystallography are normally carried out with transmission electron microscopes (TEM) as the radiation source.…”