Classification of cryo-electron sub-tomograms using constrained correlation

Cryo-electron tomography (CET) is currently the only three-dimensional imaging technique capable of visualizing macromolecules in their cellular context at close-to-native conditions with a resolution in the nanometer range. An important component for the analysis of the data is their classification, which should discriminate among various macromolecules, conformational changes and interaction partners. Missing structure factors, typically in a wedge-shaped region in Fourier space if single-axis tilting is performed, hamper classification of cryo-electron tomographic data. Here, we describe a classification method for three-dimensional (3D) sub-tomograms extracted from cryo-electron tomograms, which takes the missing wedge into account and provides reliable results. The similarity of the individually aligned sub-tomograms is scored by constrained correlation. Subsequently, they are clustered based on their pairwise correlation values. In order to demonstrate the feasibility of this approach, we apply the proposed method to simulated tomographic data of the chaperone thermosome in different conformations. By comparison of the principal components of the resulting matrix we show that the proposed metric is significantly less prone to the orientation of the missing wedge compared to the unconstrained correlation. Moreover, we apply our classification method to an experimental dataset of GroEL with and without GroES, where we achieve a distinct discrimination between the putative GroEL and GroEL/GroES complexes.