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 (3-D) structures. Rotation of 2-D images is usually done with the assumption that the magnification of the electron microscope is the same in all directions , a condition that has been found to be untrue with some electron microscopes when used with the settings necessary for cryo-EM with a direct detector device (DDD) camera (Grant and Grigorieff, in preparation). Correction of images by linear interpolation in real space has allowed high-resolution structures to be calculated from cryo-EM images for symmetric particles (Grant and Grigorieff, in preparation). Here we describe and compare a simple real 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 systematic errors . To address this problem we develop an approach to correct CTF parameters measured from distorted  images. The effect of anisotropic magnification on CTF parameters provides a simple way of detecting magnification anisotropy in cryo-EM datasets.
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 (3-D) structures. Rotation of 2-D 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 (Grant and Grigorieff, in preparation). Correction of images by linear interpolation in real space has allowed high-resolution structures to be calculated from cryo-EM images for symmetric particles (Grant and Grigorieff, in preparation). Here we describe and compare a simple real 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.
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, a condition that has been found to be untrue
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systematic errors
an apparent systematic astigmatism
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correct
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images so that they can be used with corrected