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

Min Xu,Frank Alber

doi:10.1186/1752-0509-6-s1-s18

Abstract

BackgroundCryo-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.ResultsIn 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.ConclusionsOur 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.

Highlights

Cryo-electron tomography emerges as an important component for structural system biology approaches [1,2]
One strategy to enhance the nominal resolution of the detected density maps of individual complexes is to segment the tomogram into a large number of single complex subtomograms, which are classified into similar objects by a pair-wise comparison
After subtomogram classification averaging of the aligned subtomograms in each class reveals the shapes of macromolecular complexes in each class at an increased signal-to-noise ratio (SNR), which can be assigned to the corresponding positions in the whole cell tomogram

Summary

Results

We test our methods on phantom models and actual structures of protein complexes. Pairwise alignment of subtomograms from phantom models To assess the general performance, 100 pairs of subtomograms with randomly placed phantom models were generated for different SNR levels and tilt angle ranges (Figure 2(b)). For example even when the rotational sampling is performed at only 60° intervals the stochastic iterative refinement process together with the RCS scoring produces on average errors of 3.1°, while the FCS scoring achieves 2.9° error (Table 1). The average anglular alignment errors are less than 6° even for subtomograms generated from a small tilt angle range of ±50°. We further test our alignment methods for refining the density maps of the complexes by averaging over all aligned subtomograms. We generated 1000 subtomograms (at SNR 0.5, tilt angle range ±60°) containing randomly oriented models. The resulting density maps are used to simulate 20 subtomograms for each randomly placed macromolecular complex, at SNR 0.5 and tilt angle range ±60° (Section 2.6). The distortions, as evident in the individual subtomograms are greatly reduced after averaging (Figure 6 (b))

Introduction

Methods

Conclusion

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