Algorithms for Image Restoration and 3D Reconstruction from Cryo-EM Images

Abstract

Single particle reconstruction (SPR) in cryo-electron microscopy (cryo-EM) has

recently emerged as the method of choice to determine the structure of biological

macromolecules to near atomic resolution. The typical procedure for obtaining the

final high resolution 3D structure is by starting with an initial guess and iteratively

refining it using the acquired dataset of the molecule’s 2D projection images. The

final estimate from the refinement procedure is known to often depend heavily on

the initial model used as the starting point, thereby making a good initial estimate

crucial for success.

In this thesis, we propose and test two novel approaches, which we call Orthogonal

Extension and Orthogonal Replacement, for 3D ab-initio and homology modeling in

SPR using cryo-EM and X-ray free electron lasers (XFEL). Our approach is inspired

by the molecular replacement technique used in X-ray crystallography. We first test

both approaches on noisy synthetic datasets.

Motivated by the need for a reliable estimator of the covariance matrix, we de-

velop a new image restoration method to perform contrast transfer function (CTF)

correction and denoising in a single step. Through results on several experimental

datasets, we demonstrate the efficacy of our method as a single, preliminary step to

inspect particle images, detect outliers, and estimate the covariance matrix of the un-

derlying clean images. Our covariance matrix estimator is asymptotically consistent

and successfully corrects for the CTF.

An immediate application of improved covariance estimation is an improvement

in the 2D classification or class averaging procedure in the cryo-EM pipeline. We

digress from 3D homology/ab-initio modeling to focus on this application. Since

different cryo-EM images are affected by noise as well as different CTF’s or point

spread functions from the microscope, the Euclidean distance between two images is

not an optimal metric for their affinity. We derive and test a new affinity measure

akin to the Mahalanobis distance to compare cryo-EM images belonging to different

defocus groups. We demonstrate that the new metric leads to an improvement in

nearest neighbor detection and therefore the obtained class averages.

Finally, we revisit the homology modeling procedure of Orthogonal Extension. We

incorporate our improved covariance matrix estimator into the Orthogonal Extension

algorithm and propose a family of asymptotically unbiased estimators to recover the

3D structure. We demonstrate the advantage of our estimator through numerical

experiments on synthetic and experimental datasets. We foresee this method as

a good way to provide models to initialize refinement, directly from experimental

images without performing class averaging and orientation estimation in cryo-EM

and XFEL. Our second algorithm for ab-initio modeling, Orthogonal Replacement, is

tested on synthetic datasets. In future work, Orthogonal Replacement would require

designing an appropriate experiment to collect datasets that would facilitate its usage.