III: Small: Algorithmic Tools for Spatial Positioning Studies in the Cell Nucleus

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Spatial positioning has emerged as a fundamental principle governing nuclear processes. Research on chromosome territories has indicated that the 3-D arrangement of these territories within the architecture of the cell nucleus may be closely linked to genomic function, regulation and cell differentiation. Despite this progress, the degree of non-random arrangement of chromosome territories remains unclear and no overall model at the global level has been proposed. In addition, little is known about the gene positioning inside the chromosome territories and its relationship to gene expression. This project is for developing algorithmic tools to facilitate the study of three important spatial positioning problems, (1) topology of chromosome territory, (2) chromosomes associations and spatial positioning, and (3) topological structures of associated chromosomes territories. The focus of this project is on designing efficient algorithms for several challenging computational problems which are essential for the spatial positioning problems, such as chromatic cone clustering, realization, maximum median graph, and optimal surface extraction.The project will use computational geometry techniques and optimization methods to develop a set of efficient algorithmic tools for the proposed problems. The designed and tested algorithms and techniques will be used as automatic (or semi-automatic) tools to accurately and reliably determine the spatial positioning information of genes and chromosome territories, and further elucidate the coordination of genomic expression. Algorithms from this project are also likely to be used in many other areas as information integration tools and positively impact them. This project could lead to several long term impacts. It could yield a much needed global model for studying the spatial positioning of chromosome territories and genes. The obtained algorithmic and biological results will be used to study and compare the difference of various cancer and normal cells in topological structures and associations of chromosome territories and genes. This could potentially lead to significant biological discoveries and help better understanding the mechanism of diseases (such as cancers) and their relationship to chromosome structures and associations.