Fourier-Bessel reconstruction of helical assemblies.

Helical symmetry is commonly used for building macromolecular assemblies. Helical symmetry is naturally present in viruses and cytoskeletal filaments and also occurs during crystallization of isolated proteins, such as Ca-ATPase and the nicotinic acetyl choline receptor. Structure determination of helical assemblies by electron microscopy has a long history dating back to the original work on three-dimensional (3D) reconstruction. A helix offers distinct advantages for structure determination. Not only can one improve resolution by averaging across the constituent subunits, but each helical assembly provides multiple views of these subunits and thus provides a complete 3D data set. This review focuses on Fourier methods of helical reconstruction, covering the theoretical background, a step-by-step guide to the process, and a practical example based on previous work with Ca-ATPase. Given recent results from helical reconstructions at atomic resolution and the development of graphical user interfaces to aid in the process, these methods are likely to continue to make an important contribution to the field of structural biology.