Structure determination of tubular crystals of membrane proteins. IV. Distortion correction and its combined application with real-space averaging and solvent flattening

A method for correction of three-dimensional distortions has been developed for helical assemblies and applied to tubular crystals of Ca 2 + -ATPase. This method approximates distorted helical particles with short straight segments of different orientation parameters, which are determined by fitting them to the reference data in reciprocal space. Thus, the method follows Beroukhim and Unwin [Ultramicroscopy 70 (1997) 57], but is more extended to achieve better alignment and to cope with images of poor S/N ratio. Substantial improvements were achieved by dividing the reference image into the segments of optimal lengths in exactly the same way as the test, and treating the distortions in the near and far sides of a helical particle separately. The improvement was further enhanced when combined with real-space averaging [Yonekura, Toyoshima, Ultramicroscopy 84 (2000) 15] and solvent flattening [Yonekura, Toyoshima, Ultramicroscopy 84 (2000) 29], and most pronounced when all these three were applied iteratively.