CryoEM Movie-Frame Defocus Refinement

One of the biggest advances in cryoEM recently is the invention of direct electron detectors which allow movie recording. Beam induced movement correction using movies has greatly improved the resolution of the final reconstruction (Bai et al., 2013 (link), Li et al., 2013 (link)). The movement in the X or Y direction of a micrograph is usually around several Ångstroms (e.g. 1–10 Å), while the Z-direction movement can be over a hundred Ångstroms (Russo and Passmore, 2014 (link)). Although the movement is dominantly in the Z-direction, the small movement in the XY plane severely affects the quality of cryoEM micrographs. Motion correction programs normally consider only the drift in the XY plane because the eucentric height of the object does not affect its ideal 2D projection. However, EM micrographs are modulated by CTF, which is sensitive to Z-height changes. Beam induced movement might change the CTF from frame to frame. A hundred Ångstrom movement is not a significant change even up to a 3 Å reconstruction, but Fig. 1 suggests it might help to improve a reconstruction close to 2 Å.
Accurate defocus refinement for movie frames is implemented in Gctf to deal with large movement in the Z-direction. Similar to local defocus refinement, movie defocus refinement is performed in two steps. First, global CTF parameters are determined for the averaged micrograph of motion-corrected movies. Then based on the global values, parameters for each frame are refined using an equally weighted average of adjacent frames (suggested 5–10) to reduce the noise. Two options are provided in Gctf: coherent averaging Eq. (8) or incoherent averaging Eq. (9). $|F_{i_{\mathit{ca}}}(\overrightarrow{s})|=\left|{\displaystyle \sum _{j=i-N/2}^{i+N/2}}\frac{F_j(\overrightarrow{s})}{N}\right|$ $|F_{i_{\mathit{ica}}}(\overrightarrow{s})|={\displaystyle \sum _{j=i-N/2}^{i+N/2}}\frac{|F_j(\overrightarrow{s})|}{N}$ where $|F_{i_{\mathit{ca}}}(\overrightarrow{s})|$ represents the coherent averaging of $i_{\text{th}}$ frame and $i_{\text{th}}$ the incoherent averaging; $N$ is the number of frames to be averaged.