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

Electron crystallography on multilayered three-dimensional microcrystals has been limited in application by the need to define precisely the three-dimensional shape of the diffraction density profiles. A new method is presented here to obtain this profile from experimental spot positions which are shifted in a characteristic way from the expected Bragg positions. While the Bragg positions are defined by the diffraction geometry, the characteristic shift additionally depends on the density profile 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.