Direct detector device (DDD) cameras have revolutionized single particle electron cryomicroscopy (cryo-EM) of protein complexes . In addition to increasing the detective quantum efficiency with which images can be recorded , acquisition of DDD movies during exposures allows for correction of movement of the specimen, due both to instabilities in the specimen stage of the microscope and electron beam-induced movement. Unlike specimen stage drift, beam-induced movement is not always homogeneous within an image. Local correlation in the trajectories of nearby particles suggests that beam-induced motion is due to deformation of the ice layer. Algorithms have already been described that can correct movement of entire frames or large regions of frames at exposures of 2-3 e^{- rolling averages to be calculated from frames and fit linear trajectories for particles. Here we describe an algorithm that allows for individual < 1 MDa particle images to be aligned without frame averaging when imaged with 2.5 e^{- . The algorithm maximizes the overall correlation of the shifted frames with the sum of the shifted frames. The optimum in this single objective function is found efficiently by making use of analytically calculated derivatives of the function. Two additional measures are implemented to smooth estimates of particle trajectories . First , rapid changes in particle positions between frames are penalized . Second, weighted averaging of nearby trajectories ensures local correlation in trajectories. DDD movies of the\textit{Saccharomyces cerevisiae V-ATPase are used to demonstrate that the algorithm is able to produce physically reasonable trajectories for a 900 kDa membrane protein complex .
Direct detector device (DDD) cameras have revolutionized single particle electron cryomicroscopy (cryo-EM) . In addition to an improved camera detective quantum efficiency , acquisition of DDD movies allows for correction of movement of the specimen, due both to instabilities in the microscope specimen stage and electron beam-induced movement. Unlike specimen stage drift, beam-induced movement is not always homogeneous within an image. Local correlation in the trajectories of nearby particles suggests that beam-induced motion is due to deformation of the ice layer. Algorithms have already been described that can correct movement for large regions of frames and for > 1 MDa protein particles. Another algorithm allows individual < 1 MDa protein particle trajectories to be estimated, but requires rolling averages to be calculated from frames and fits linear trajectories for particles. Here we describe an algorithm that allows for individual < 1 MDa particle images to be aligned without frame averaging or linear trajectories . The algorithm maximizes the overall correlation of the shifted frames with the sum of the shifted frames. The optimum in this single objective function is found efficiently by making use of analytically calculated derivatives of the function. To smooth estimates of particle trajectories , rapid changes in particle positions between frames are penalized in the objective function and weighted averaging of nearby trajectories ensures local correlation in trajectories. \textit{ This individual particle motion correction, in combination with weighting of Fourier components to account for increasing radiation damage in later frames, can be used to improve 3-D maps from single particle cryo-EM .
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