A collaborative framework for 3 D alignment and classification of heterogeneous subvolumes in cryo-electron tomography

1047-8477/$ see front matter Published by Elsevier http://dx.doi.org/10.1016/j.jsb.2012.10.010 ⇑ Corresponding author. E-mail addresses: subramas@mail.nih.gov (S. Sub o@duke.edu (G. Sapiro). The limitation of using low electron doses in non-destructive cryo-electron tomography of biological specimens can be partially offset via averaging of aligned and structurally homogeneous subsets present in tomograms. This type of sub-volume averaging is especially challenging when multiple species are present. Here, we tackle the problem of conformational separation and alignment with a ‘‘collaborative’’ approach designed to reduce the effect of the ‘‘curse of dimensionality’’ encountered in standard pairwise comparisons. Our new approach is based on using the nuclear norm as a collaborative similarity measure for alignment of sub-volumes, and by exploiting the presence of symmetry early in the processing. We provide a strict validation of this method by analyzing mixtures of intact simian immunodeficiency viruses SIV mac239 and SIV CP-MAC. Electron microscopic images of these two virus preparations are indistinguishable except for subtle differences in conformation of the envelope glycoproteins displayed on the surface of each virus particle. By using the nuclear norm-based, collaborative alignment method presented here, we demonstrate that the genetic identity of each virus particle present in the mixture can be assigned based solely on the structural information derived from single envelope glycoproteins displayed on the virus surface. Published by Elsevier Inc.