A strategy for the reconstruction of structures possessing axial symmetry: sectioned axonemes in sperm flagella

Abstract

The images of complex biological structures seen in the electron microscope, possessing an n-fold rotational symmetry, can be enhanced by averaging the axially repeating motif in order to improve their signal-to-noise ratio; this requires that the slices with n-fold symmetry do not exhibit distortions relative to one another. A strategy is proposed to detect the relative distortions and to remove them in order to obtain reliable results from the averaging process. Extensive use is made of cross-correlation analysis and of interpolation; because the procedure involves iterated resampling of the image, it is essential to adopt interpolation algorithms which preserve the spectral power. The procedure is illustrated by the analysis of transverse sections of the sperm flagellum axoneme of a stick insect; it might be used for the reconstruction of microtubules, nuclear pore complexes, virus capsids, and other supramolecular aggregates. The reconstructed images of axoneme sections reveal new information about the interactions between adjacent doublets; in particular, a double conjunction connecting the inner dynein arm with the nearest B-tubule has been consistently observed.