Three-dimensional reconstruction methods in Single Particle Analysis from transmission electron microscopy data.

The Transmission Electron Microscope provides two-dimensional (2D) images of the specimens under study. However, the architecture of these specimens is defined in a three-dimensional (3D) coordinate space, in volumetric terms, making the direct microscope output somehow "short" in terms of dimensionality. This situation has prompted the development of methods to quantitatively estimate 3D volumes from sets of 2D images, which are usually referred to as "three-dimensional reconstruction methods". These 3D reconstruction methods build on four considerations: (1) The relationship between the 2D images and the 3D volume must be of a particularly simple type, (2) many 2D images are needed to gain 3D volumetric information, (3) the 2D images and the 3D volume have to be in the same coordinate reference frame and (4), in practical terms, the reconstructed 3D volume will only be an approximation to the original 3D volume which gave raise to the 2D projections. In this work we will adopt a quite general view, trying to address a large community of interested readers, although some sections will be particularly devoted to the 3D analysis of isolated macromolecular complexes in the application area normally referred to as Single Particle Analysis (SPA).