Common lines modeling for reference free ab-initio reconstruction in
  cryo-EM

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Abstract

We consider the problem of estimating an unbiased and reference-free ab-inito model for non-symmetric molecules from images generated by single-particle cryo-electron microscopy. The proposed algorithm finds the globally optimal assignment of orientations that simultaneously respects all common lines between all images. The contribution of each common line to the estimated orientations is weighted according to a statistical model for common lines' detection errors. The key property of the proposed algorithm is that it finds the global optimum for the orientations given the common lines. In particular, any local optima in the common lines energy landscape do not affect the proposed algorithm. As a result, it is applicable to thousands of images at once, very robust to noise, completely reference free, and not biased towards any initial model. A byproduct of the algorithm is a set of measures that allow to asses the reliability of the obtained ab-initio model. We demonstrate the algorithm using class averages from two experimental data sets, resulting in ab-initio models with resolutions of 20A or better, even from class averages consisting of as few as three raw images per class.

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Three-dimensional reconstruction from a single-exposure, random conical tilt series applied to the 50S ribosomal subunit of Escherichia coli.

Stephan A. Verschoor, Steven Frank, T Wagenknecht … (1987)

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).