Due to low labeling efficiency and structural heterogeneity in fluorescence-based single-molecule localization microscopy (SMLM), image alignment and quantitative analysis is often required to make accurate conclusions on the spatial relationships between proteins. Cryo-electron microscopy (EM) image alignment procedures have been applied to average structures taken with super-resolution microscopy. However, unlike cryo-EM, the much larger cellular structures analyzed by super-resolution microscopy are often heterogeneous, resulting in misalignment. And the light-microscopy image library is much smaller, which makes classification challenging. To overcome these two challenges, we developed a method to deform semi-flexible ring-shaped structures and then align the 3D structures without classification. These algorithms can register semi-flexible structures with an accuracy of several nanometers in short computation time and with greatly reduced memory requirements. We demonstrated our methods by aligning experimental Stochastic Optical Reconstruction Microscopy (STORM) images of ciliary distal appendages and simulated structures. Symmetries, dimensions, and locations of protein complexes in 3D are revealed by the alignment and averaging for heterogeneous, tilted, and under-labeled structures.
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