Mahalanobis Distance for Class Averaging of Cryo-EM Images

Single particle reconstruction (SPR) from cryo-electron microscopy (EM) is a technique in which the 3D structure of a molecule needs to be determined from its contrast transfer function (CTF) affected, noisy 2D projection images taken at unknown viewing directions. One of the main challenges in cryo-EM is the typically low signal to noise ratio (SNR) of the acquired images. 2D classification of images, followed by class averaging, improves the SNR of the resulting averages, and is used for selecting particles from micrographs and for inspecting the particle images. We introduce a new affinity measure, akin to the Mahalanobis distance, to compare cryo-EM images belonging to different defocus groups. The new similarity measure is employed to detect similar images, thereby leading to an improved algorithm for class averaging. We evaluate the performance of the proposed class averaging procedure on synthetic datasets, obtaining state of the art classification.Comment: Final version accepted to the 14th IEEE International Symposium on Biomedical Imaging (ISBI 2017

Improved methods for single-particle cryogenic electron microscopy

Biological macromolecules such as enzymes are nanoscale machines. This is true in a concrete sense: if the atomic structure of a biological macromolecule can be obtained, the theories of mechanics and intermolecular forces can be applied to explain how the machine works in terms that engineers would understand, including motors, ratchets, gates and transducers. Nevertheless, biological macromolecules are complex, fragile and extremely small, so obtaining their structures is a challenging experimental endeavor. Single-particle cryogenic electron microscopy (cryo-EM) is a technique for determining the 3D structure of a biological macromolecule from a large set of 2D electron micrographs of individual structurally-identical particles. To obtain such images, a solution of the macromolecules must be prepared in the frozen-hydrated state, embedded in a thin electron-transparent glassy film of water. This specimen must then be imaged with a very short exposure to avoid radiation damage. A powerful computer must then be used to sort, align, and average the 2D particle images to back-calculate the 3D structure. At its best, cryo-EM can determine the structures of biological macromolecules to atomic resolution. In practice, this goal is usually not achieved. Cryo-EM has gotten significantly more powerful in the past few years due to improvements in equipment and methodology. Several of the most significant advances originated in the labs of David Agard and Yifan Cheng at UCSF. When I began my PhD with Yifan, the spirit in the lab was that cryo-EM could keep getting better and better: with enough engineering, determining the 3D structure of an arbitrary biological macromolecule would be as routine an experiment as gel electrophoresis or DNA sequencing. Inspired, I took on projects in the lab that I thought would move the field closer to that goal. In the first chapter of this thesis, I describe work I did supporting a project initiated by David Agard and his long-time scientific programmer Shawn Zheng. They developed and implemented an algorithm, MotionCor2, for correcting the complex, anisotropic movements that occur when a frozen-hydrated specimen interacts with the high-energy electron beam. My role was to benchmark MotionCor2 on a panel of real-world 3D reconstruction tasks. I was able to show that MotionCor2 restored the highest resolution details in the images, ultimately yielding significantly better structures than simpler algorithms. For me, this projected highlighted the importance of benchmarking an algorithm for use in routine real-world conditions with the right metrics. In chapter 1, I include the manuscript for the MotionCor2 study, formatted to highlight my contributions that were moved to the supplement in the original publication by Nature Methods. One of the major remaining issues with cryo-EM is sample preparation: preparing the thin freestanding films of frozen-hydrated particles necessarily exposes those particles to air-water interfaces. Many fragile macromolecular complexes denature when exposed to such interfaces, preventing structure determination with cryo-EM. In chapters 2 and 3, I describe my efforts to develop a simple, robust approach to stabilizing fragile macromolecular complexes during the vitrification process. In chapter 2, I develop a method for coating EM grids with an electron-transparent and functionalizable graphene-oxide support film. I demonstrate that such GO grids are compatible with high-resolution structure determination. This work was published in the Journal of Structural Biology in 2018. In chapter 3, I extend this work by functionalizing GO grids with nucleic acids, enabling routine structure determination of uncrosslinked chromatin specimens. In on-going work, I used nucleic acid grids to solve high-resolution structures of a highly fragile specimen, the snf2h-nucleosome complex, and analyzed the conformational heterogeneity of the nucleosome substrate. These results were made possible by the nucleic acid grid, as the other major approach for stabilizing chromatin specimens, chemical crosslinking, not work for this specimen.Perhaps the most fundamental problem with single-particle cryo-EM is the radiation sensitivity of frozen-hydrated macromolecules. To image biological matter with electrons is to destroy it, so obtaining images of undamaged specimens requires very short, highly under sampled exposures. The resultant images are extremely noisy and low contrast, with most particles barely visible from the background. In chapter 4, I describe a novel computational approach to generating contrast in cryo-EM. Using a recently described machine learning strategy for training a parameterized denoising algorithm, I developed a computer program, restore, that denoises cryo-EM images, greatly enhancing their contrast and interpretability. This program leverages recent advances in computer vision and deep learning which have not yet been widely used in cryo-EM image processing algorithms. To characterize the performance of the algorithm on real-world data, I extended conventional metrics for image resolution to measure how an arbitrary transformation affects images at different spatial frequencies. These novel metrics are general and may be useful for characterizing other nonlinear reconstruction algorithms in cryo-EM and medical imaging. Finally, I showed that denoised cryo-EM images maintain the high-resolution information required for accurate 3D reconstruction. Denoising can be applied to conventional cryo-EM images and can be reversed whenever necessary. I have made the software for restore program publicly available and have submitted a manuscript for peer-reviewed publication

Manifold Rewiring for Unlabeled Imaging

Geometric data analysis relies on graphs that are either given as input or inferred from data. These graphs are often treated as "correct" when solving downstream tasks such as graph signal denoising. But real-world graphs are known to contain missing and spurious links. Similarly, graphs inferred from noisy data will be perturbed. We thus define and study the problem of graph denoising, as opposed to graph signal denoising, and propose an approach based on link-prediction graph neural networks. We focus in particular on neighborhood graphs over point clouds sampled from low-dimensional manifolds, such as those arising in imaging inverse problems and exploratory data analysis. We illustrate our graph denoising framework on regular synthetic graphs and then apply it to single-particle cryo-EM where the measurements are corrupted by very high levels of noise. Due to this degradation, the initial graph is contaminated by noise, leading to missing or spurious edges. We show that our proposed graph denoising algorithm improves the state-of-the-art performance of multi-frequency vector diffusion maps