Angle determination for side views in single particle electron microscopy

In order to build a first model in single particle electron microscopy the relative angular orientation of each image of a protein complex must be determined. These orientations can be described by three Eulerian angles. Images of complexes that present the same view can be aligned in two-dimensions and averaged in order to increase their signal-to-noise ratio. Based on these averaged images, several standard approaches exist for determining Euler angles for randomly oriented projection images. The common lines and angular reconstitution methods work well for particles with symmetry while the random conical tilting and related orthogonal tilt reconstruction methods work in most cases but require the acquisition of tilt pairs of images. For the situation where views of particles can be identified that are rotations about a single axis parallel to the grid, an alternative algorithm to determine the orientations of class averages without the need to acquire tilt pairs can be applied. This type of view of a complex is usually called a side view. This paper describes the detailed workings and characterization of an algorithm, named rotational analysis, which uses real-space fiducial markers derived from the averages themselves to determine the Euler angles for side views. We demonstrate how this algorithm works in practice by applying it to a data set of images of affinity-purified bovine mitochondrial ATP synthase.