Contours in Visualization

This thesis studies the visualization of set collections either via or defines as the relations among contours. In the first part, dynamic Euler diagrams are used to communicate and improve semimanually the result of clustering methods which allow clusters to overlap arbitrarily. The contours of the Euler diagram are rendered as implicit surfaces called blobs in computer graphics. The interaction metaphor is the moving of items into or out of these blobs. The utility of the method is demonstrated on data arising from the analysis of gene expressions. The method works well for small datasets of up to one hundred items and few clusters. In the second part, these limitations are mitigated employing a GPU-based rendering of Euler diagrams and mixing textures and colors to resolve overlapping regions better. The GPU-based approach subdivides the screen into triangles on which it performs a contour interpolation, i.e. a fragment shader determines for each pixel which zones of an Euler diagram it belongs to. The rendering speed is thus increased to allow multiple hundred items. The method is applied to an example comparing different document clustering results. The contour tree compactly describes scalar field topology. From the viewpoint of graph drawing, it is a tree with attributes at vertices and optionally on edges. Standard tree drawing algorithms emphasize structural properties of the tree and neglect the attributes. Adapting popular graph drawing approaches to the problem of contour tree drawing it is found that they are unable to convey this information. Five aesthetic criteria for drawing contour trees are proposed and a novel algorithm for drawing contour trees in the plane that satisfies four of these criteria is presented. The implementation is fast and effective for contour tree sizes usually used in interactive systems and also produces readable pictures for larger trees. Dynamical models that explain the formation of spatial structures of RNA molecules have reached a complexity that requires novel visualization methods to analyze these model\''s validity. The fourth part of the thesis focuses on the visualization of so-called folding landscapes of a growing RNA molecule. Folding landscapes describe the energy of a molecule as a function of its spatial configuration; they are huge and high dimensional. Their most salient features are described by their so-called barrier tree -- a contour tree for discrete observation spaces. The changing folding landscapes of a growing RNA chain are visualized as an animation of the corresponding barrier tree sequence. The animation is created as an adaption of the foresight layout with tolerance algorithm for dynamic graph layout. The adaptation requires changes to the concept of supergraph and it layout. The thesis finishes with some thoughts on how these approaches can be combined and how the task the application should support can help inform the choice of visualization modality

Recombineering in mycobacteria using mycobacteriophage proteins

Genetic manipulations of Mycobacterium tuberculosis are complicated by its slow growth, inefficient DNA uptake, and relatively high levels of illegitimate recombination. Most methods for construction of gene replacement mutants are lengthy and complicated, and the lack of generalized transducing phages that infect M. tuberculosis prevents simple construction of isogenic mutant strains. Characterization and genomic analysis of mycobacteriophages has provided numerous molecular and genetic tools for the mycobacteria. Recently, genes encoding homologues of the Escherichia coli Rac prophage RecET proteins were revealed in the genome of mycobacteriophage Chec9c. RecE and RecT are functional analogues of the phage λ Red recombination proteins, Exo (exonuclease) and Beta (recombinase), respectively. These recombination enzymes act coordinately to promote high levels of recombination in vivo in E. coli and related bacteria using short regions of homology, facilitating the development of a powerful genetic technique called 'recombineering.' Biochemical characterization of Che9c gp60 and gp61 demonstrated that they possess exonuclease and DNA binding activities, respectively, similar to RecET and λ Exo/Beta. Expression of gp60/gp61 in M. smegmatis and M. tuberculosis substantially increases homologous recombination such that 90% of recovered colonies are the desired gene replacement mutants. Further development of this system demonstrated that Che9c gp61 facilitates introduction of selectable and non-selectable point mutations on mycobacterial genomes at high frequencies using short (<50 nt) ssDNA substrates. The mycobacterial recombineering system provides a simple and efficient method for mutagenesis with minimal DNA manipulation. While it is clear that similar phage-encoded recombinase homologues are rare, they can be readily identified by genomic studies and by in vivo characterization. Several putative recombination systems have been identified in mycobacteriophages Halo, BPs, and Giles, and recombineering of drug-resistance point mutations provides an easy assay for recombinase activity. Analysis of recombinases from various phages – including λ Beta and E. coli RecT – indicates that these proteins function best in their native bacteria. The mycobacteriophage-encoded proteins exhibited varying levels of activity, suggesting that analysis of multiple proteins is required to achieve optimal recombination frequencies. The apparent species-specific nature of these recombinases suggests the recombineering technology could likely be extended to any bacterial system through characterization of host-specific bacteriophages

Solving Challenging Structures using Single-Particle Cryogenic Electron Microscopy

Single-particle cryogenic electron microscopy (cryo-EM) has become a powerful mainstay tool in high resolution structural biology thanks to advances in hardware, software and sample preparation technology. In my thesis, I utilized this technique to unravel the function of various challenging biological macromolecules. My first focus was bacterial ribosomal biogenesis: understanding how bacteria assemble their ribosomes. Ribosomes are the factories of the cell, responsible for manufacturing all proteins. Ribosomes themselves are huge, with the bacterial version made of 52 proteins and 4566 RNA nucleotides. How these components assemble has long been a mystery. Early groundbreaking work sketched out a biogenesis pathway using purified components in vitro – but under non-physiological conditions. We sought to understand how the bacterial ribosome – specifically the large subunit 50S – is built inside the cell. To achieve this, we engineered a conditional knock-out bacterial strain that lacked one specific ribosomal protein (L17). This caused the cells to accumulate incomplete intermediates along the 50S biogenesis pathway. These intermediates were purified and examined with mass spectrometry and single-particle cryo-EM. Two major hurdles arose in this project: firstly, the biogenesis intermediates exhibited a preferred orientation when vitrified for cryo-EM analysis. This means that instead of showing many different views required for reconstruction of the 3D structure, the intermediates only adopted one view on the cryo-EM grid. To overcome this problem, we engineered a method to induce additional views on the microscope by tilting the stage. Using another test protein that also exhibited preferred orientation (hemagglutinin), we optimized and characterized this new tilt methodology and showed it was generally applicable to overcoming preferred orientation, regardless of type of specimen. We also created a software tool, called 3DFSC (3dfsc.salk.edu), for other microscopists to calculate the degree of directional anisotropy in their structures due to preferred orientation. Using this tilt strategy finally enabled the structural elucidation of our 50S intermediates. The second challenge in the project was the large amount of heterogeneity present in the sample. Through hierarchical 3D classification schemes using the latest software tools, we obtained 14 different 50S intermediate structures, all from imaging a single cryo-EM grid. By analyzing the missing components of each intermediate, and corroborating these observations with mass spectrometry data, we outlined the first in vivo 50S assembly pathway, and showed that ribosome assembly occurs step-wise and in parallel pathways. My second focus was on pushing the resolution limits of single-particle cryo-EM using adeno-associated virus (AAV) serotype 2 homogeneous virus-like particles (VLPs) that lack DNA. Exploiting several technical advances to improve resolution, including use of gold grids, per-particle CTF refinement, and correction for Ewald sphere curvature, we managed to obtain a 1.86 Å resolution reconstruction of the AAV2L336C variant VLP, the highest resolution icosahedral virus reconstruction solved by single-particle cryo-EM to date. Using our structure, we were able to show improvements using Ewald sphere curvature correction and shed light on the mechanistic basis as to why the L336C mutation resulted in defects in genome packaging and infectivity compared to the WT viral particles. My third focus was the understanding of small membrane proteins involved in infectious diseases. Membrane proteins are a challenge to work with due to the need for them to be extracted from the lipid bilayer for studies as compared to soluble proteins. Infectious diseases have a huge burden on society, with the top three infectious agents accounting for 2.7 million deaths in 2016. The third most deadly infectious disease is malaria, a mosquito-borne parasite which kills 450,000 people annually. One drug used early on for treating malaria was chloroquine but its usefulness waned due to development of resistance. Chloroquine resistance is mediated by the chloroquine resistance transporter (PfCRT). Although small (49 kDa) for single-particle cryo-EM, we solved its structure by using fragment antibody technology to add mass and help with image alignment and 3D reconstruction. The 3.2 Å structure resembles other drug metabolite transporters, and the chloroquine resistance mutations map to a ring around the central cavity, suggesting this central pore as the drug binding site. Tuberculosis (TB) is the top killer, above malaria and HIV/AIDS, being responsible for 1.3 million deaths. In TB, a common antibiotic target is the bacterium’s cell wall synthesis machinery. One family of such enzymes is the arabinosyltransferases, which synthesize the critical arabinose sugars. Using single-particle cryo-EM, we solved two high resolution structures of one such essential enzyme, AftD. Due to the low yield of the protein, a picoliter automated sample dispensing robot was crucial to allow for initial cryo-EM analysis. We then performed mutagenesis studies in M. smegmatis, a TB model organism, which uncovered the critical amino acid residues in the active site and determined that a bound acyl-carrier-protein was likely involved in allosteric inhibition of AftD’s active site. Another member of the family, EmbB, is the target of a widely used frontline TB drug called ethambutol. We have solved the high resolution structures of the apo and putative drug-bound states of EmbB, allowing us to map out, for the first time, both the active site and drug-resistance mutations of this crucial enzyme. The atomic structures of the functional pockets of Mycobacterial AftD and malarial PfCRT will hopefully enable structure-based drug design to improve existing drugs or potentially even develop new treatments against these infectious maladies. In conclusion, the continual and breathtaking improvements in single-particle cryo-EM methodology has been instrumental in allowing the elucidation of the aforementioned biological macromolecules from ribosome biogenesis intermediates, to AAV2 vehicle, Plasmodium drug resistance transporter to mycobacterial glycosyltransferases – structures of which help explain biological function

FORMULAE AND ASYMPTOTICS FOR COEFFICIENTS OF ALGEBRAIC FUNCTIONS

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