Description and comparison of algorithms for correcting anisotropic magnification in cryo-EM images

Single particle electron cryomicroscopy (cryo-EM) allows for structures of proteins and protein complexes to be determined from images of non-crystalline specimens. Cryo-EM data analysis requires electron microscope images of randomly oriented ice-embedded protein particles to be rotated and translated to allow for coherent averaging when calculating three-dimensional (3D) structures. Rotation of 2D images is usually done with the assumption that the magnification of the electron microscope is the same in all directions. However, due to electron optical aberrations, this condition is not met with some electron microscopes when used with the settings necessary for cryo-EM with a direct detector device (DDD) camera. Correction of images by linear interpolation in real space has allowed high-resolution structures to be calculated from cryo-EM images for symmetric particles. Here we describe and compare a simple real space method, a simple Fourier space method, and a somewhat more sophisticated Fourier space method to correct images for a measured anisotropy in magnification. Further, anisotropic magnification causes contrast transfer function (CTF) parameters estimated from image power spectra to have an apparent systematic astigmatism. To address this problem we develop an approach to adjust CTF parameters measured from distorted images so that they can be used with corrected images. The effect of anisotropic magnification on CTF parameters provides a simple way of detecting magnification anisotropy in cryo-EM datasets.We are grateful to Alexis Rohou and Timothy Grant from Nikolaus Grigorie 's laboratory, who quickly put us on the correct track when we noticed the apparent systematic astigmatism in plots of z1 versus z2. We thank Richard Henderson for critical comments on the manuscript. JZ was supported by a Doctoral Postgraduate Scholarship from the National Science and Engineering Council of Canada and a Mary Gertrude l'Anson Scholarship. JLR was supported by a Canada Research Chair. This work was funded by NSERC grant 401724-12 to JLR