Structure determination of tubular crystals of membrane proteins. II. Averaging of tubular crystals of different helical classes

A set of programs has been developed for averaging the data from tubular crystals belonging to different helical classes. This was done either by (i) cutting out molecules constituting a unit cell from density maps, and aligning and averaging them in real space; (ii) transforming the densities in a unit cell to layer-line data according to a (possibly artificial) helical symmetry, aligning and averaging them in reciprocal space. These methods were applied to tubular crystals of Ca2+-ATPase. Either method worked well and substantially improved the data quality. Transforming the reconstructed images to the layer-line data has many advantages and is essential for fully exploiting the power of averaging.