A statistically harmonized alignment-classification in image space enables accurate and robust alignment of noisy images in single particle analysis.

In determining the three-dimensional (3D) structure of macromolecular assemblies in single particle analysis, a large representative dataset of two-dimensional (2D) average images from huge number of raw images is a key for high resolution. Because alignments prior to averaging are computationally intensive, currently available multireference alignment (MRA) software does not survey every possible alignment. This leads to misaligned images, creating blurred averages and reducing the quality of the final 3D reconstruction. We present a new method, in which multireference alignment is harmonized with classification (multireference multiple alignment: MRMA). This method enables a statistical comparison of multiple alignment peaks, reflecting the similarities between each raw image and a set of reference images. Among the selected alignment candidates for each raw image, misaligned images are statistically excluded, based on the principle that aligned raw images of similar projections have a dense distribution around the correctly aligned coordinates in image space. This newly developed method was examined for accuracy and speed using model image sets with various signal-to-noise ratios, and with electron microscope images of the Transient Receptor Potential C3 and the sodium channel. In every data set, the newly developed method outperformed conventional methods in robustness against noise and in speed, creating 2D average images of higher quality. This statistically harmonized alignment-classification combination should greatly improve the quality of single particle analysis.