Class Averaging in Cryo-EM Single Particle Reconstruction

Abstract

Single-particle reconstruction of vitrified samples (cryogenic electron microscopy, or

cryo-EM) provides structural information for a large variety of biological molecules,

ranging from small proteins to large macromolecular assemblies in their native state,

without the need to produce crystals. However, for common-lines based ab initio

modeling, it is a great challenge to produce density maps, because of the low signal

to noise ratio (SNR) of the projection images. A crucial step is alignment and

averaging of the 2D projection images, which are from similar viewing directions, a

procedure known as "class averaging". Images from the same projection angles should

be identified, aligned and averaged to achieve a higher signal-to-noise ratio.

In Chapter 2, we introduce a set of rotationally invariant adaptive basis to compress

and denoise the projection images. The global alignment followed by clustering

has been a common practice to generate class averages for the past 20 years. In Chapter

3, we show that due to the geometry and topology of the image data set, it is

impossible to globally align all images. The commonly used reference-free alignment

procedure unavoidably introduces errors. We then introduce a fast in-plane rotationally

invariant viewing angle classification method for identifying, among a large

number of projection images, similar views without prior knowledge of the molecule

to alleviate the computational burden for pairwise alignment and classification. To

improve the initial classification results, we introduce the class averaging matrix in

Chapter 4. The spectral properties of class averaging matrix allow us to define new

metrics between projection images, which are more robust to noise. Class averaging

operator is a special case of vector diffusion maps (VDM), which takes into account

the linear transformation between data points. In Chapter 5, we discuss the application

of VDM in class averaging. We are able to reconstruct ab initio 3D electron

density maps with high resolution for experimental data sets, using the class averaging

procedure described in this thesis and the common-lines reconstruction algorithm.