Robust evaluation of 3D electron cryomicroscopy data using tilt-pairs

Determining the structure of a protein complex using electron microscopy requires the calculation of a 3D density map from 2D images of single particles. Since the individual images are taken at low electron dose to avoid radiation damage, they are noisy and difficult to align with each other. This can result in incorrect maps, making validation essential. Pairs of electron micrographs taken at known angles to each other (tilt-pairs) can be used to measure the accuracy of assigned projection orientations and verify the soundness of calculated maps. Here we establish a statistical framework for evaluating images and density maps using tilt-pairs. The directional distribution of such angular data is modelled using a Fisher distribution on the unit sphere. This provides a simple, quantitative and easily comparable metric, the concentration parameter κ, for evaluating the quality of datasets and density maps that is independent of the data collection and analysis methods. A large κ is indicative of good agreement between the particle images and the 3D density map. For structure validation, we recommend κ>10 and a p-value <0.01. The statistical framework herein allows one to objectively answer the question: Is a reconstructed density map correct within a particular confidence interval?