An algorithm for estimation and correction of anisotropic magnification distortion of cryo-EM images without need of pre-calibration.

Anisotropic magnification distortion of TEM images (mainly the elliptic distortion) has been recently found as a potential resolution-limiting factor in single particle 3-D reconstruction. Elliptic distortions of ∼1-3% have been reported for multiple microscopes under low magnification settings (e.g., 18,000×), which significantly limited the achievable resolution of single particle 3-D reconstruction, especially for large particles. Here we report a generic algorithm that formulates the distortion correction problem as a generalized 2-D alignment task and estimates the distortion parameters directly from the particle images. Unlike the present pre-calibration methods, our computational method is applicable to all datasets collected at a broad range of magnifications using any microscope without need of additional experimental measurements. Moreover, the per-micrograph and/or per-particle level elliptic distortion estimation in our method could resolve potential distortion variations within a cryo-EM dataset, and further improve the 3-D reconstructions relative to constant-value correction by the pre-calibration methods. With successful applications to multiple datasets and cross-validation with the pre-calibration method, we have demonstrated the validity and robustness of our algorithm in estimating the distortion; correction of the elliptic distortion significantly improved the achievable resolutions by ∼1-3 folds and enabled 3-D reconstructions of multiple viral structures at 2.4-2.6Å resolutions. The resolution limits with elliptic distortion and the amounts of resolution improvements with distortion correction were found to strongly correlate with the product of the particle size and the amount of distortion, which can help assess if elliptic distortion is a major resolution limiting factor for single particle cryo-EM projects.