Viewing Angle Classification of Cryo-Electron Microscopy Images Using Eigenvectors

Abstract

The cryo-electron microscopy (cryo-EM) reconstruction problem is to find the three-dimensional structure of a macromolecule given noisy versions of its two-dimensional projection images at unknown random directions. We introduce a new algorithm for identifying noisy cryo-EM images of nearby viewing angles. This identification is an important first step in three-dimensional structure determination of macromolecules from cryo-EM, because once identified, these images can be rotationally aligned and averaged to produce “class averages” of better quality. The main advantage of our algorithm is its extreme robustness to noise. The algorithm is also very efficient in terms of running time and memory requirements, because it is based on the computation of the top few eigenvectors of a specially designed sparse Hermitian matrix. These advantages are demonstrated in numerous numerical experiments.

Cross-Validation of Data Compatibility Between Small Angle X-ray Scattering and Cryo-Electron Microscopy

“…The improvement of SNR usually has been done either by class averaging, that is, averaging many different images in a class corresponding to similar orientations (van Heel and Frank, 1981;van Heel, 1984;Schatz and Van Heel, 1990;Penczek et al, 1992;Penczek, 2002;Scheres et al, 2005;Park et al, 2011;Singer et al, 2011;Shkolnisky and Singer, 2012;Park and Chirikjian, 2014;Zhao and Singer, 2014), or by applying denoising techniques, such as bilateral filtering ( Jiang et al, 2003) sinograms (Mielikäinen and Ravantti, 2005) and covariance Wiener filtering (Bhamre et al, 2016) to EM images. Note that the method we propose in this work is to remove the noise on a single image rather than over a class, which makes our work very different from others.…”

Moment-Based Angular Difference Estimation Between Two Tomographic Projections in 2D and 3D

“…As in 2D, the angular difference in 3D can also be calculated by means of the projection direction estimation. In particular, the method proposed in [23] gives good estimation results at very low SNR (smaller than −10 dB) and clearly outperforms the results of MADE. Nevertheless, the advantage of our method is that it can be used with a small number of projections, whereas the method in [23] needs a sufficiently large number of projections (≥ 10000) in order to obtain a good result.…”

“…In particular, the method proposed in [23] gives good estimation results at very low SNR (smaller than −10 dB) and clearly outperforms the results of MADE. Nevertheless, the advantage of our method is that it can be used with a small number of projections, whereas the method in [23] needs a sufficiently large number of projections (≥ 10000) in order to obtain a good result. Another family of direction estimation methods uses the common line technique [8,15,17,27].…”

“…The authors would like to thank Hau-Tieng Wu and Zhi-Zhen Zhao for sharing their codes on projection direction estimation in 2D [22] and in 3D [23]. This work was supported by RHODES project ANR-14-CE27-0012.…”

A Local Clustering Algorithm for Connection Graphs

“…Some early usage of connection graphs can be traced back to work in graph gauge theory for computing the vibrational spectra of molecules and examining spins associated with vibrations [9]. There have been more recent developments of related research in principal component analysis [13], cryo-electron microscopy [11,15], angular synchronization of eigenvectors [10,14], and vector diffusion maps [16]. In computer vision, there has been a great deal of work dealing with the many photos that are available on the web, in which information networks of photos can be built.…”