Reconstruction of Three Dimensional Structures from Electron Micrographs: The Equivalence of Two Methods

Abstract

A transmission electron micrograph is to a good degree of approximation a projection of a three dimensional structure. Provided that a sufficient number of projections are available, it is possible to reconstruct a three dimensional structure which is consistent with the projections. Among the methods which have been proposed for generating a three dimensional structure from projections, two methods alone produce single, unique structures which are consistent, in a least squares sense, with the projections from which they are derived.The first of these was demonstrated by DeRosier and Klug in a reconstruction of the tail of the bacteriophage T4. Their technique is illustrated in figure 1. A three dimensional structure, represented by the duck, is Fourier transformed to yield a three dimensional Fourier transform. (Fourier transformation is a mathematical operation readily performed on a digital computer.) An inverse Fourier transformation exists and the Fourier transform of the duck may be inversely transformed to recreate the three dimensional duck structure.