Multi-class maximum likelihood symmetry determination and motif reconstruction of 3-D helical objects from projection images for electron microscopy

摘要

Many micro- to nano-scale 3-D biological objects have a helical symmetry. Cryo electron microscopy provides 2-D projection images where, however, the images have low SNR and unknown projection directions. The object is described as a helical array of identical motifs, where both the parameters of the helical symmetry and the motif are unknown. Using a detailed image formation model, a maximum likelihood estimator for the parameters of the symmetry and the 3-D motif based on images of many objects and algorithms for computing the estimate are described. The possibility that the objects are not identical but rather come from a small set of homogeneous classes is included. The first example is based on 316 128×100 pixel experimental images of Tobacco Mosaic Virus, has one class, and achieves 12.40Å spatial resolution in the reconstruction. The second example is based on 400 128 × 128 pixel synthetic images of helical objects constructed from NaK ion channel pore macromolecular complexes, has two classes differing in helical symmetry, and achieves 7.84Å and 7.90Å spatial resolution in the reconstructions for the two classes.