Common lines ab-initio reconstruction of D2D_2-symmetric molecules

Cryo-electron microscopy is a state-of-the-art method for determining high-resolution three-dimensional models of molecules, from their two-dimensional projection images taken by an electron microscope. A crucial step in this method is to determine a low-resolution model of the molecule using only the given projection images, without using any three-dimensional information, such as an assumed reference model. For molecules without symmetry, this is often done by exploiting common lines between pairs of images. Common lines algorithms have been recently devised for molecules with cyclic symmetry, but no such algorithms exist for molecules with dihedral symmetry. In this work, we present a common lines algorithm for determining the structure of molecules with $D_{2}$ symmetry. The algorithm exploits the common lines between all pairs of images simultaneously, as well as common lines within each image. We demonstrate the applicability of our algorithm using experimental cryo-electron microscopy data

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

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

Multi-Dimensional Data Analysis and Processing in Electron-Induced Microanalysis

The new facilities offered by computer controlled data capturing devices allow one to open the field of data acquisition from one or two-dimensional spaces to multi-dimensional ones. The methods used for analysing and processing such data sets have to move in parallel towards multi-dimensionality. Multivariate Statistical Analysis is one of the tools which appear to be promising in : data analysis, data reduction, data processing (multivariate noise filtering), data interpolation and extrapolation. Illustrations of these different possibilities are given in the fields of spatially resolved spectroscopy, time-dependent spectroscopy and elemental mapping from Electron Energy Loss Spectroscopy

Breaking symmetry

Polarity is a fundamental feature of almost all cells. It generally refers to the asymmetric organization of several cellular components. The plasma membrane, for example, exhibits both a transbilayer and a lateral asymmetry in most eukaryotic cells. Lipids are asymmetrically distributed between the cytoplasmic and the extracellular leaflet of the membrane and segregate laterally together with specific proteins to form dynamic nanoscale assemblies, known as rafts. Polarity can also specifically describe the asymmetric distribution of key molecules within a cell. These molecules, known as polarity determinants, can orient a multitude of specialized cellular functions, such as cell shape, cell division and fate determination. In the framework of this thesis, we aimed to reconstitute essential features of membrane unmixing and cell polarity with a "bottom-up" synthetic biology approach. We worked with both: pure lipid systems, whose unmixing is driven by the asymmetric distribution of lipids in the two leaflets, and a lipid-protein system, whose polarization is instead due to reaction-diffusion mechanisms. In both cases, we used Giant Unilamellar Vesicles (GUVs) and Sup- ported Lipid Bilayers (SLBs) to model biological membranes and employed modern biophys- ical techniques, such as fluorescence correlation spectroscopy, to quantitatively characterize lipid bilayers and protein-lipid interactions. In the pure lipid systems, we first reconstituted membrane transbilayer asymmetry, applying a cyclodextrin-mediated lipid exchange method, which enables us to enrich membranes with lipids of choice. The enrichment of the membrane with sphingomyelin and/or cholesterol triggers the segregation of lipids into two coexisting asymmetric phases both in SLBs and GUVs, whereas exchanging different amounts of phosphatidylglycerol with the outer leaflet of the GUV membranes controls vesicle shape. Tuning the lipid content of model membranes revealed that small changes in the composition of one leaflet affect the overall lipid miscibility of the bilayer and that membrane shape transformations are possible also in absence of a protein machinery and as a consequence of the lipid redistribution in the membrane. In the protein-lipid system, we aimed to reconstitute a minimal polarization system inspired by the C. elegans embryo at one-cell stage, which polarize along the anterior-posterior axis by sorting the PARtitioning defective (PAR) proteins into two distinct cortical domains. In this system polarity is maintained by the mutual inhibition between anterior (aPARs: PAR-3, PAR-6 and PKC-3) and posterior (pPARs: PAR-1, PAR-2 and LGL-1) PARs, which reciprocally antagonize their binding to the cortex, mutually excluding each other. We focused on LGL-1, which acts directly on PAR-6. Submitting LGL-1 to model membranes allowed us to identify a conserved region of the protein that binds negatively-charged membranes and to determine its lipid binding affinity and specificity. Selected LGL-1 mutants were then gen- erated to better understand the electrostatic mechanism involved in the membrane binding. LGL-1 was finally combined with PKC-3 to generate a functional membrane binding switch.Polarität ist eine Grundeigenschaft fast aller Zellen und bezeichnet die asymmetrische Organ- isation verschiedener zellulärer Bestandteile. Zum Beispiel besitzt die Zellmembran bei den meisten eukaryotischen Zellen sowohl eine Asymmetrie zwischen als auch innerhalb der Lipid- schichten. Das heißt, Lipide sind asymmetrisch in der zytoplasmatischen und der extrazel- lulären Lipidschicht der Membran verteilt und bilden zusammen mit spezifischen Proteinen auf lateraler Ebene dynamisch-geordnete Nanostrukturen, sogenannte Lipid Rafts. Polarität kann zudem die asymmetrische Verteilung bestimmter Schlüsselmoleküle innerhalb einer Zelle beschreiben. Diese als Polaritätsdeterminanten bekannten Moleküle bedingen eine Vielfalt spezieller Zellfunktionen so wie z.B. Zellform, Zellteilung und Zellschicksal. Diese Arbeit versucht wesentliche Eigenschaften von Zell- und Membranpolarität mit Hilfe des sogenannten “Bottom-up”-Ansatzes (“von unten nach oben”) der synthetischen Biologie nachzubilden. Es wurden zwei Systeme etabliert, um Polarisation mit Minimalsystemen zu reproduzieren. Zum einen reine Lipidsysteme, deren Polarisation durch die asymmetrische Verteilung von Lipiden in den zwei Lipidschichten entsteht, zum anderen Lipid-Proteinsysteme, deren Polarisation sich stattdessen aus Reaktions-Diffusions Mechanismen herleitet. In beiden Fällen wurden Riesenvesikel (GUVs) sowie gestützte Lipiddoppelschichten (SLBs) für die Modellierung biologischer Membranen verwendet und moderne biophysikalische Techniken, wie die Fluoreszenz-Korrelations-Spektroskopie, für eine quantitative Charakterisierung von Lipiddoppelschichten und Protein-Lipid Interaktionen angewendet. Um die Asymmetrie der Membrandoppelschicht in reinen Lipidsystemen zu rekonstruieren, wurde eine Anreicherung einer der Lipidschichten der Membran mit den gewünschten Lipiden durch Anwendung eines mit Cyclodextrin kontrollierten Lipidaustauschprotokolls vorgenommen. Die Anreicherung der Membran mit Sphingomyelin und/oder Cholesterol induzierte die Aufteilung der Lipide in zwei koexistierende, asymmetrische Phasen sowohl in SLBs als auch GUVs. Die Vesikelform hingegen wurde durch den Austausch verschiedener Mengen Phosphatdylglycerol in deräusseren Lipidschicht der GUV-Membranen verändert. Eine Anpassung des Lipidgehaltes von Membranen im Modellsystem zeigte, dass kleine Änderungen in der Zusammensetzung einer Lipidschicht die Mischbarkeit der Lipide der Doppelschicht beeinflusst und dass Formveränderungen der Membran, selbst in Abwesenheit eines Proteingerüstes, als Konsequenz einer Lipidumverteilung in der Membran möglich sind. Im Protein-Lipid System wurde die Nachbildung eines Minimalpolarisationssystems angestrebt, wie man es beim C. elegans Embryo im Einzellstadium beobachten kann. Dieser wird durch Anordnung der PARtitioning defective (PAR) Proteine in zwei unterschiedliche kortikale Bereiche entlang der Vorder-Hinterachse polarisiert. In dem PAR-System wird die Polarität durch gegenseitige Inhibition der vorderen (aPARs: PAR-3, PAR-6 und PKC-3) und hinteren (pPARs: PAR-1, PAR-2 und LGL-1) PAR-Proteine aufrechterhalten. Diese hemmen die gegenseitige Bindung an den Kortex. Da LGL-1 direkt auf PAR-6 einwirkt, wurde es als potentielles Schüsselmolekül der Zellpolarization in künstlichen Membranen rekonstruiert. Durch Rekonstruktion von LGL-1 in Membranmodellen konnte die konservierte Region des Proteins, die mit negativ geladenen Membranen interagiert, sowie dessen Bindungsanität und -Spezifität gegenüber Lipiden quantitativ gemessen werden. Darauf folgend wurden LGL- 1 Mutationen hergestellt, um die bei der Membranbindung auftretenden elektrostatischen Mechanismen besser zu verstehen. Zuletzt wurden LGL-1 und PKC-3 kombiniert, um die Membranbindung von LGL-1 reproduzierbar zu inhibieren