Classification and 3D averaging with missing wedge correction in biological electron tomography

Abstract

Strategies for the determination of 3D structures of biological macromolecules using electron crystallography and single-particle electron microscopy utilize powerful tools for the averaging of information obtained from 2D projection images of structurally homogeneous specimens. In contrast, electron tomographic approaches have often been used to study the 3D structures of heterogeneous, one-of-a-kind objects such as whole cells where image-averaging strategies are not applicable. Complex entities such as cells and viruses, nevertheless, contain multiple copies of numerous macromolecules that can individually be subjected to 3D averaging. Here we present a complete framework for alignment, classification, and averaging of volumes derived by electron tomography that is computationally efficient and effectively accounts for the missing wedge that is inherent to limited-angle electron tomography. Modeling the missing data as a multiplying mask in reciprocal space we show that the effect of the missing wedge can be accounted for seamlessly in all alignment and classification operations. We solve the alignment problem using the convolution theorem in harmonic analysis, thus eliminating the need for approaches that require exhaustive angular search, and adopt an iterative approach to alignment and classification that does not require the use of external references. We demonstrate that our method can be successfully applied for 3D classification and averaging of phantom volumes as well as experimentally obtained tomograms of GroEL where the outcomes of the analysis can be quantitatively compared against the expected results.

Trimeric HIV-1 glycoprotein gp140 immunogens and native HIV-1 envelope glycoproteins display the same closed and open quaternary molecular architectures

“…Earlier cryoelectron tomographic studies of the structure of native Env displayed on intact virions (2,3) were helped by the fact that the bilayer membrane provides a reference point to define the approximate initial orientation of the spike in the tomograms, thereby restricting the initial search of relative orientations of individual spikes to two angular parameters. The structural findings we report here represent a validated generalization of this 3D classification and averaging approach (28) to soluble protein complexes where there is no prior information on the orientation, and demonstrates its utility for the structural analysis of small protein complexes, such as HIV-1 gp140 trimers.…”

“…In conventional cryoelectron microscopy, structure determination is based on assembling the 3D structure by averaging the structural information present in a large number of individual 2D projection images, whose relative orientations are determined iteratively starting from an initial 3D model at lower resolution. In contrast, structure determination using cryoelectron tomography relies on averaging of 3D molecular images, with the model building steps combined with assignment of relative orientations (28). Earlier cryoelectron tomographic studies of the structure of native Env displayed on intact virions (2,3) were helped by the fact that the bilayer membrane provides a reference point to define the approximate initial orientation of the spike in the tomograms, thereby restricting the initial search of relative orientations of individual spikes to two angular parameters.…”

“…0.7 to 3.8 μm. Three-dimensional structures of unliganded gp140 trimers and associated complexes were obtained using cryoelectron tomography combined with classification and 3D subvolume averaging implementing procedures described in Bartesaghi et al (28) and White et al (3). Illustration of image classes obtained for unliganded and liganded gp140 trimers are presented in Figs.…”

Structure and accessibility of HA trimers on intact 2009 H1N1 pandemic influenza virus to stem region-specific neutralizing antibodies

“…Spike subvolumes (100 3 voxels) were automatically extracted from viral surfaces as described previously (47). Alignment, classification, and 3D averaging of the extracted spike volumes were carried out using essentially the same principles as described previously (32,48). For separation of unliganded and liganded spikes, we used a collaborative alignment and clustering algorithm based on the concept of minimizing matrix rank and its convex surrogate, the nuclear norm (33), to derive the structures of liganded HA complexes.…”

“…The 3D structures derived in Fig. 3 were obtained using threefold symmetrization of the HA-trimer-containing subvolumes, as in our previous structural analyses of antibody-bound envelope glycoprotein spikes on intact HIV (32,33). Compared with HIV, in which the glycoproteins are sparsely packed on the viral membrane, HA trimers are much more densely packed, with an average spacing of ∼14 nm (Fig.…”