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.

Study of the relation between the shape of lacosamide crystals and the composition of crystallization medium

Crystallization is the critical process used by pharmaceutical industries to achieve the desired size, size distribution, shape and polymorphism of a product material. Control of these properties presents a major challenge since they influence considerably downstream processing factors. Experimental work aimed at finding ways to control the crystal shape of Lacosamide, an active pharmaceutical ingredient developed by UCB Pharma, during crystallization was carried out. It was found that the crystal lattice displayed a very strong unidirectional double hydrogen bonding, which was at the origin of the needle shape of the Lacosamide crystals. Two main strategies were followed to hinder the hydrogen bonding and compete with the addition of a Lacosamide molecule along the crystal length axis: changing the crystallization medium or weakening the hydrogen bonding. Various solvents were tested to check whether the solvent used to crystallize Lacosamide had an influence on the final crystal shape. Solvent molecules seemed to slow down the growth in the length axis by hindering the unidirectional hydrogen bonding of Lacosamide crystals, but not enough to promote the crystal growth in the width axis. Additives were also tested. Certain additives have shown to compete in a more efficient way than solvent molecules with the hydrogen bonding of Lacosamide. The additive effect has also shown to be compatible with the solvent effect. In parallel, hydrogen atoms in Lacosamide were changed into deuterium atoms in order to weaken the hydrogen bonds strength. Weakening the hydrogen bonds of Lacosamide allowed to let the crystal grow in the width axis. Deuteration was found to be combinable with solvent effect while being in competition with the additive effect. The Lacosamide molecule was eventually deemed an absolute needle by the terms of Lovette and Doherty. The results of this dissertation are aimed at contributing to this classification.