  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. 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.
