High precision alignment of cryo-electron subtomograms through gradient-based parallel optimization

Cryo-electron tomography emerges as an important component for structural system biology. It not only allows the structural characterization of macromolecular complexes, but also the detection of their cellular localizations in near living conditions. However, the method is hampered by low resolution, missing data and low signal-to-noise ratio (SNR). To overcome some of these difficulties and enhance the nominal resolution one can align and average a large set of subtomograms. Existing methods for obtaining the optimal alignments are mostly based on an exhaustive scanning of all but discrete relative rigid transformations (i.e. rotations and translations) of one subtomogram with respect to the other.

In this paper, we propose gradient-guided alignment methods based on two popular subtomogram similarity measures, a real space as well as a Fourier-space constrained score. We also propose a stochastic parallel refinement method that increases significantly the efficiency for the simultaneous refinement of a set of alignment candidates. We estimate that our stochastic parallel refinement is on average about 20 to 40 fold faster in comparison to the standard independent refinement approach. Results on simulated data of model complexes and experimental structures of protein complexes show that even for highly distorted subtomograms and with only a small number of very sparsely distributed initial alignment seeds, our combined methods can accurately recover true transformations with a substantially higher precision than the scanning based alignment methods.

Our methods increase significantly the efficiency and accuracy for subtomogram alignments, which is a key factor for the systematic classification of macromolecular complexes in cryo-electron tomograms of whole cells.