Statistical methods for polyhedral shape classification with incomplete data - application to cryo-electron tomographic images

A certain type of bacterial inclusion, known as a bacterial microcompartment, was recently identified and imaged through cryo-electron tomography. A reconstructed 3D object from single-axis limited angle tilt-series cryo-electron tomography contains missing regions and this problem is known as the missing wedge problem. Due to missing regions on the reconstructed images, analyzing their 3D structures is a challenging problem. The existing methods overcome this problem by aligning and averaging several similar shaped objects. These schemes work well if the objects are symmetric and several objects with almost similar shapes and sizes are available. Since the bacterial inclusions studied here are not symmetric, are deformed, and show a wide range of shapes and sizes, the existing approaches are not appropriate. This research develops new statistical methods for analyzing geometric properties, such as volume, symmetry, aspect ratio, polyhedral structures etc., of these bacterial inclusions in presence of missing data. These methods work with deformed and non-symmetric varied shaped objects and do not necessitate multiple objects for handling the missing wedge problem. The developed methods and contributions include: (a) an improved method for manual image segmentation, (b) a new approach to 'complete' the segmented and reconstructed incomplete 3D images, (c) a polyhedral structural distance model to predict the polyhedral shapes of these microstructures, (d) a new shape descriptor for polyhedral shapes, named as polyhedron profile statistic, and (e) the Bayes classifier, linear discriminant analysis and support vector machine based classifiers for supervised incomplete polyhedral shape classification. Finally, the predicted 3D shapes for these bacterial microstructures belong to the Johnson solids family, and these shapes along with their other geometric properties are important for better understanding of their chemical and biological characteristics.

The application of aryne chemistry and use of α-diazo carbonyl derivatives in indazole synthesis with biological evaluation

This thesis outlines the synthetic chemistry involved in the preparation of a range of novel indazole compounds and details the subsequent investigation into their potential as biologically active agents. The synthetic route utilised in this research to form the indazole structure was the [3+2] dipolar cycloaddition of diazo carbonyl compounds with reactive aryne intermediates generated in situ. The preparation of further novel indazole derivatives containing different functional groups and substituents was performed by synthesising alternative 1,3- dipole and dipolarophile analogues and provided additionally diverse compounds. Further derivatisation of the indazole product was made possible by deacylation and alkylation methods. Transformation reactions were performed on alkenecontaining ester side chains to provide novel epoxide, aldehyde and tertiary amine derivatives. The first chapter is a review of the literature beginning with a short overview on the structure, reactivity and common synthetic routes to diazo carbonyl derivatives. More attention is given to the use of diazo compounds as 1,3-dipoles in cycloaddition reactions or where the diazo group is incorporated into the final product. A review of the interesting background, structure and reactivity of aryne intermediates is also presented. In addition, some common syntheses of indazole compounds are presented as well as a brief discussion on the importance of indazole compounds as therapeutic agents. The second chapter discusses the synthetic routes employed towards the synthesis of the range of indazoles. Initially, the syntheses of the diazo carbonyl and aryne precursors are described. Next, the synthetic methods to prepare the indazole compounds are provided followed by discussion on derivatisation of the indazole compounds including N-deacylation, N-benzylation and ester side-chain transformation of some alkene-containing indazoles. A series of novel indazole derivatives were submitted for anti-cancer screening at the U.S National Cancer Institute (NCI). A number of these derivatives were identified as hit compounds, with excellent growth inhibition. The results obtained from biological evaluation from the NCI are provided with further results pending from the Community for Open Antimicrobial Drug Discovery. The third chapter details the full experimental procedures, including spectroscopic and analytical data for all the compounds prepared during this research.