Methods for aligning and for averaging 3D volumes with missing data.

The visibility and resolution of a tomographic reconstruction containing multiple copies of discrete particles can be enhanced by averaging subtomograms after they are corrected aligned. However, the "missing wedge" in electron tomography can easily lead to erroneous alignment. We have explored a Fourier space cross-correlation method with a proper weighting scheme to align and average different sets of volumetric data, each of which has different missing data due to the limited specimen tilts. This approach depends neither on a preexisting template, nor an exact knowledge of the geometry, orientation, or amount of the missing data. This paper introduces a procedure where the missing data might be gradually "filled in" by consecutively aligning and averaging volumes with different orientations of their missing data. We have validated these techniques by a set of simulated data with various symmetries and extent of missing data. We have also successfully applied these procedures to experimental cryo-electron tomographic data [Chang, J.T., Schmid, M.F., Rixon, F.J., and Chiu, W., 2007. Electron cryotomography reveals the portal in the herpesvirus capsid. J. Virol. 81, 2065-2068; Schmid, M.F., Paredes, A.M., Khant, H.A., Soyer, F., Aldrich, H.C., Chiu, W., and Shively, J.M., 2006. Structure of Halothiobacillus neapolitanus carboxysomes by cryo-electron tomography. J. Mol. Biol. 364, 526-535].