Validity domain of the weak-phase-object approximation for electron diffraction of thin protein crystals

The domain of validity of the weak-phase-object (WPO) approximation is evaluated for high-energy electrons (100 keV, 500 keV and 1 MeV) scattered by crystalline biological macromolecules. Cytochrome b5 is used as an example in which calculated dynamical diffraction intensities are used to simulate observed diffraction intensities which are then compared with intensities calculated by the weak-phase-object approximation. Three criteria of validity are used, namely the crystallographic residual (R value), the interpretability of difference Patterson maps, and the results of phasing by the heavy-atom isomorphous replacement method. The present calculations indicate that the error associated with the WPO approximation is quite acceptable up to a specimen thickness of 200 A for 100 keV electrons, which is two to four times the thickness limit for crystalline organic structures with much smaller unit-cell dimensions. An equally acceptable thickness limit at 500 keV and 1MeV is about 300-350 A.