Methods for three-dimensional reconstruction of heterogeneous assemblies.

Electron microscopy (EM) has developed into an important method for determining the three-dimensional (3D) structures of biological complexes, in particular of isolated macromolecular complexes in vitrified solution (cryo-EM of "single particles"). One of the consequences of studying complexes in solution rather than in a crystal lattice is that they are less constrained to adopt a single conformation. It is a common problem in single-particle analysis that samples of purified macromolecules can be structurally heterogeneous, with molecules adopting different conformations, corresponding to different functional states. In the case of multisubunit assemblies, there may also be heterogeneity of assembly or ligand binding. Heterogeneity limits the accuracy and resolution of 3D structures, since different conformations will contribute to a single 3D map and variable parts of the structure will be smeared out. Therefore, a new group of image processing methods has been developed to deal with the problems of detecting and sorting structural heterogeneity. The basic problem is to discriminate the source of image variations, and then to separate the images into homogeneous subsets for separate reconstruction. Variations in image features can arise from different particle orientations, variations in conformation and/or ligand binding, and noise fluctuations in the low signal-to-noise ratio images typical of cryo-EM. Here, we present a review of approaches developed to deal with these problems, along with examples of the application of a method based on multivariate statistical analysis to both model and real data. The methods have been used to discriminate small differences in size, conformation and ligand binding, and to obtain high quality, reliable reconstructions of multiple structures from mixed data sets.