Michael Radermacher

To overcome the radiation damage-induced limitations to the resolution of three-dimensional reconstructions from electron microscopic tilt series, novel reconstruction schemes have been developed that require only a single exposure of the specimen. The tilt series collected with these methods have random projection directions. First, three-dimensional reconstruction techniques are described that are applicable to data obtained from tilt series with regular tilt geometry, followed by the extensions of these techniques to permit analysis of projection series with randomly spaced tilts. The main emphasis is placed on the weighted back-projection methods, which have recently been extended so as to be applicable to random tilt series. Besides a description of the algorithms, the complete procedure for a three-dimensional reconstruction from a single-exposure, random conical tilt series is explained, including the determination of the azimuthal angles, the alignment scheme for conical tilt series, the dependence of the achievable resolution on the number of projections for regular conical and single-axis geometries, and the method to calculate the actual resolution of two-dimensional image averages and of three-dimensional reconstructions using the phase residual and Fourier ring correlation criteria. Examples are given of biological specimens to which these three-dimensional reconstruction methods have been applied.

We present a new reconstruction method that takes advantage of the fact that many biological macromolecular assemblies show a preferred orientation with respect to the plane of the specimen grid in the electron microscopic preparation. From one micrograph taken of such a specimen tilted by a large angle, a conical tilt series with random azimuthal angles can be extracted and used for a three-dimensional reconstruction. Our technique allows the determination of the molecular structure under low-dose conditions, which are not achievable with reconstruction methods that use conventional tilt series. The reconstruction method combines a number of existing image processing techniques with a newly developed weighted back-projection algorithm designed for three-dimensional reconstruction from projections taken with arbitrary projecting directions. The method is described as it was applied to the three-dimensional reconstruction of the structure of the 50S ribosomal subunit of Escherichia coli (E. coli).