Jeremy Grant

Date of Award

2008

Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Arts (MA)

Department

Mathematics

Advisor

Andre Khalil

Second Committee Member

David Bradley

Third Committee Member

William O. Bray

Abstract

Interphase chromosomes are organized into discrete chromosome territories (CTs) that may occupy preferred sub-nuclear positions. While chromosome size and gene density appear to influence positioning, the biophysical mechanisms behind CT localization, especially the relationship between morphology and positioning, remain obscure. One reason for this has been the difficulty in imaging, segmenting, and analyzing structures with variable or imprecise boundaries. This prompted us to develop a novel approach, based on the two-dimensional (2D) wavelet-transform modulus maxima (WTMM) method, adapted to perform objective and rigorous CT segmentation from nuclear background. The wavelet-transform acts as a mathematical microscope to characterize spatial image information over a continuous range of size scales. This space-scale nature, combined with full objectivity of the formalism, makes it more accurate than intensity-based segmentation algorithms and more appropriate than manual intervention. Using the WTMM method in two dimensions, we show that CTs have a highly nonspherical 3D morphology, that CT positioning is nonrandom, and favors heterologous CT groupings. Once we have fully developed and tested the method in two dimensions, we modify it to perform three-dimensional segmentation and reconstruction of c. elegans embryonic nuclei. The c. elegans nematode provides an opportunity to study cellular development at the molecular level in a rather narrow temporal frame. Interest in automated cell lineage tracing in c. elegans has led to the development of systems to perform this function using intensity thresholding image analysis techniques on time-lapse 3D images of histone-GFP labeled cells/nuclei. We attempt to improve this process by using the 2D WTMM method developed to segment mouse CTs. We modify the method to find and segment any number of objects within a particular size range (on the order of cell nuclei) in an image. We perform this segmentation on every image in a 3D image stack of GFP-fluoresced widefield images and then automatically sort these segmented objects into individual nuclei folders with the goal of recreating the 3D nuclei spheres.

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