Angular Reconstitution in Three-dimensional Electron Microscopy: Historical and Theoretical Aspects

Angular reconstitution in combination with multivariate statistical techniques to classify and average the characteristic views of a molecule form a complete, selfcontained methodology for the high-resolution threedimensional (3D) structure analysis of uncrystallized macromolecules by electron microscopy. The angular reconstitution approach is based on the fact that two different two-dimensional (2D) projections of a 3D object always have a one-dimensional (1D) line projection in common. From the angles between such common-line projections, the relative Euler angle orientations of projections can be determined. Our single-particle electron microscopical approach has already yielded structures to resolution levels of ~10Å and no theoretical resolution limits are yet in sight. The angular reconstitution approach was first presented ten years ago. A decade later, we can invoke hindsight to discuss the development of angular reconstitution in its historical context.