Novel computational methods for in vitro and in situ cryo-electron microscopy

Over the past decade, advances in microscope hardware and image data processing algorithms have made cryo-electron microscopy (cryo-EM) a dominant technique for protein structure determination. Near-atomic resolution can now be obtained for many challenging in vitro samples using single-particle analysis (SPA), while sub-tomogram averaging (STA) can obtain sub-nanometer resolution for large protein complexes in a crowded cellular environment. Reaching high resolution requires large amounts of im-age data. Modern transmission electron microscopes (TEMs) automate the acquisition process and can acquire thousands of micrographs or hundreds of tomographic tilt se-ries over several days without intervention. In a first step, the data must be pre-processed: Micrographs acquired as movies are cor-rected for stage and beam-induced motion. For tilt series, additional alignment of all micrographs in 3D is performed using gold- or patch-based fiducials. Parameters of the contrast-transfer function (CTF) are estimated to enable its reversal during SPA refine-ment. Finally, individual protein particles must be located and extracted from the aligned micrographs. Current pre-processing algorithms, especially those for particle picking, are not robust enough to enable fully unsupervised operation. Thus, pre-processing is start-ed after data collection, and takes several days due to the amount of supervision re-quired. Pre-processing the data in parallel to acquisition with more robust algorithms would save time and allow to discover bad samples and microscope settings early on. Warp is a new software for cryo-EM data pre-processing. It implements new algorithms for motion correction, CTF estimation, tomogram reconstruction, as well as deep learn-ing-based approaches to particle picking and image denoising. The algorithms are more accurate and robust, enabling unsupervised operation. Warp integrates all pre-processing steps into a pipeline that is executed on-the-fly during data collection. Inte-grated with SPA tools, the pipeline can produce 2D and 3D classes less than an hour into data collection for favorable samples. Here I describe the implementation of the new algorithms, and evaluate them on various movie and tilt series data sets. I show that un-supervised pre-processing of a tilted influenza hemagglutinin trimer sample with Warp and refinement in cryoSPARC can improve previously published resolution from 3.9 Å to 3.2 Å. Warp’s algorithms operate in a reference-free manner to improve the image resolution at the pre-processing stage when no high-resolution maps are available for the particles yet. Once 3D maps have been refined, they can be used to go back to the raw data and perform reference-based refinement of sample motion and CTF in movies and tilt series. M is a new tool I developed to solve this task in a multi-particle framework. Instead of following the SPA assumption that every particle is single and independent, M models all particles in a field of view as parts of a large, physically connected multi-particle system. This allows M to optimize hyper-parameters of the system, such as sample motion and deformation, or higher-order aberrations in the CTF. Because M models these effects accurately and optimizes all hyper-parameters simultaneously with particle alignments, it can surpass previous reference-based frame and tilt series alignment tools. Here I de-scribe the implementation of M, evaluate it on several data sets, and demonstrate that the new algorithms achieve equally high resolution with movie and tilt series data of the same sample. Most strikingly, the combination of Warp, RELION and M can resolve 70S ribosomes bound to an antibiotic at 3.5 Å inside vitrified Mycoplasma pneumoniae cells, marking a major advance in resolution for in situ imaging

Boosted ab initio Cryo-EM 3D Reconstruction with ACE-EM

The central problem in cryo-electron microscopy (cryo-EM) is to recover the 3D structure from noisy 2D projection images which requires estimating the missing projection angles (poses). Recent methods attempted to solve the 3D reconstruction problem with the autoencoder architecture, which suffers from the latent vector space sampling problem and frequently produces suboptimal pose inferences and inferior 3D reconstructions. Here we present an improved autoencoder architecture called ACE (Asymmetric Complementary autoEncoder), based on which we designed the ACE-EM method for cryo-EM 3D reconstructions. Compared to previous methods, ACE-EM reached higher pose space coverage within the same training time and boosted the reconstruction performance regardless of the choice of decoders. With this method, the Nyquist resolution (highest possible resolution) was reached for 3D reconstructions of both simulated and experimental cryo-EM datasets. Furthermore, ACE-EM is the only amortized inference method that reached the Nyquist resolution

Advances in image processing for single-particle analysis by electron cryomicroscopy and challenges ahead

Electron cryomicroscopy (cryo-EM) is essential for the study and functional understanding of non-crystalline macromolecules such as proteins. These molecules cannot be imaged using X-ray crystallography or other popular methods. CryoEM has been successfully used to visualize molecules such as ribosomes, viruses, and ion channels, for example. Obtaining structural models of these at various conformational states leads to insight on how these molecules function. Recent advances in imaging technology have given cryo-EM a scientific rebirth. Because of imaging improvements, image processing and analysis of the resultant images have increased the resolution such that molecular structures can be resolved at the atomic level. Cryo-EM is ripe with stimulating image processing challenges. In this article, we will touch on the most essential in order to build an accurate structural three-dimensional model from noisy projection images. Traditional approaches, such as k-means clustering for class averaging, will be provided as background. With this review, however, we will highlight fresh approaches from new and varied angles for each image processing sub-problem, including a 3D reconstruction method for asymmetric molecules using just two projection images and deep learning algorithms for automated particle picking. Keywords: Cryo-electron microscopy, Single Particle Analysis, Image processing algorithms

Extracting the Structure and Conformations of Biological Entities from Large Datasets

In biology, structure determines function, which often proceeds via changes in conformation. Efficient means for determining structure exist, but mapping conformations continue to present a serious challenge. Single-particles approaches, such as cryogenic electron microscopy (cryo-EM) and emerging diffract & destroy X-ray techniques are, in principle, ideally positioned to overcome these challenges. But the algorithmic ability to extract information from large heterogeneous datasets consisting of unsorted snapshots - each emanating from an unknown orientation of an object in an unknown conformation - remains elusive. It is the objective of this thesis to describe and validate a powerful suite of manifold-based algorithms able to extract structural and conformational information from large datasets. These computationally efficient algorithms offer a new approach to determining the structure and conformations of viruses and macromolecules. After an introduction, we demonstrate a distributed, exact k-Nearest Neighbor Graph (k-NNG) construction method, in order to establish a firm algorithmic basis for manifold-based analysis. The proposed algorithm uses Graphics Processing Units (GPUs) and exploits multiple levels of parallelism in distributed computational environment and it is scalable for different cluster sizes, with each compute node in the cluster containing multiple GPUs. Next, we present applications of manifold-based analysis in determining structure and conformational variability. Using the Diffusion Map algorithm, a new approach is presented, which is capable of determining structure of symmetric objects, such as viruses, to 1/100th of the object diameter, using low-signal diffraction snapshots. This is demonstrated by means of a successful 3D reconstruction of the Satellite Tobacco Necrosis Virus (STNV) to atomic resolution from simulated diffraction snapshots with and without noise. We next present a new approach for determining discrete conformational changes of the enzyme Adenylate kinase (ADK) from very large datasets of up to 20 million snapshots, each with ~104 pixels. This exceeds by an order of magnitude the largest dataset previously analyzed. Finally, we present a theoretical framework and an algorithmic pipeline for capturing continuous conformational changes of the ribosome from ultralow-signal (-12dB) experimental cryo-EM. Our analysis shows a smooth, concerted change in molecular structure in two-dimensional projection, which might be indicative of the way the ribosome functions as a molecular machine. The thesis ends with a summary and future prospects

Structural Variability from Noisy Tomographic Projections

In cryo-electron microscopy, the 3D electric potentials of an ensemble of molecules are projected along arbitrary viewing directions to yield noisy 2D images. The volume maps representing these potentials typically exhibit a great deal of structural variability, which is described by their 3D covariance matrix. Typically, this covariance matrix is approximately low-rank and can be used to cluster the volumes or estimate the intrinsic geometry of the conformation space. We formulate the estimation of this covariance matrix as a linear inverse problem, yielding a consistent least-squares estimator. For $n$ images of size $N$-by-$N$ pixels, we propose an algorithm for calculating this covariance estimator with computational complexity $\mathcal{O}(nN^4+\sqrt{\kappa}N^6 \log N)$, where the condition number $\kappa$ is empirically in the range $10$--$200$. Its efficiency relies on the observation that the normal equations are equivalent to a deconvolution problem in 6D. This is then solved by the conjugate gradient method with an appropriate circulant preconditioner. The result is the first computationally efficient algorithm for consistent estimation of 3D covariance from noisy projections. It also compares favorably in runtime with respect to previously proposed non-consistent estimators. Motivated by the recent success of eigenvalue shrinkage procedures for high-dimensional covariance matrices, we introduce a shrinkage procedure that improves accuracy at lower signal-to-noise ratios. We evaluate our methods on simulated datasets and achieve classification results comparable to state-of-the-art methods in shorter running time. We also present results on clustering volumes in an experimental dataset, illustrating the power of the proposed algorithm for practical determination of structural variability.Comment: 52 pages, 11 figure