Comments on Three-Dimensional Reconstruction and Averaging
The aim of one of the first papers  on three-dimensional microscopy ([1,2,3]) was the structure determination crystals of native biomolecules. The first prerequisite was to develop methods for the artifact-free preparation of crystals in such a way that they would resist the high vaeuum in the electron microscope. The problem was resolved by the replacement of the water (about 50%!) inside the cross-linked crystals with the monomer of a hydrophilic plastic (Aquon, Durcopan, Polymethacrylate, etc. (see also ) and subsequent polymerization. This polymer matrix contains the molecules in the ordered array of the protein crystal. Such a “plastified” crystal not only resists the high vaeuum in the microscope but can also be cut into arbitrarily oriented sections with the aid of an ultra-microtome, thereby facilitating the collection of three-dimensional data. The preservation of the crystal in the different preparation steps was checked by X-ray precession photographs of the crystals. The “test crystals” — myoglobin and erythroeruorine — retained their high order (reflexions up to a resolution of better than 0.2 nm!), even after complete replacement of the water by the monomer. But the poly-merization partially distorts the regulär array of the molecules, obviously by forces which link the monomer molecules to the polymer chains. The final resolution depends on the polymerization proeess. It varies from 0.4 nm to 0.8 nm — thus allowing in principle electron microscopical structure determination up to the same resolution limit. It has been demonstrated in  by electron diffraction that the intensity relations of the electron diffraction reflexes are approximately the same as the intensity relations of the corresponding X-ray intensities, thus proving that indeed native molecules have scattered in context with the kinematical theory and in context with the “averaging principle” in ag- gregates which allows — as first pointed out in paper  — a complete elimination of the influence of radiation damage.
KeywordsConical Angle Partial Projection Dimensional Crystal Reciprocal Lattice Point Aperiodic Case
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