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

空间定位已成为控制核过程的一项基本原则。对染色体区域的研究表明，这些区域在细胞核结构中的三维排列可能与基因组功能、调控和细胞分化密切相关。尽管取得了这一进展，但染色体区域的非随机排列程度仍不清楚，也没有提出全球水平的整体模型。此外，对染色体区域内的基因定位及其与基因表达的关系知之甚少。 该项目旨在开发算法工具，以促进三个重要的空间定位问题的研究，（1）染色体区域的拓扑结构，（2）染色体关联和空间定位，以及（3）相关染色体区域的拓扑结构。本计画的重点是针对空间定位问题中的几个具有挑战性的计算问题，例如色锥聚类、实现、最大中值图、最佳曲面抽取等，设计有效的演算法，并利用计算几何技术与最佳化方法，发展出一套有效的演算工具。设计和测试的算法和技术将被用作自动（或半自动）工具，以准确可靠地确定基因和染色体区域的空间定位信息，并进一步阐明基因组表达的协调性。该项目的算法也可能被用于许多其他领域，作为信息集成工具，并对其产生积极影响。该项目可能会产生一些长期影响。它可以产生一个急需的全球模型，研究染色体领土和基因的空间定位。所获得的算法和生物学结果将用于研究和比较各种癌症和正常细胞在拓扑结构以及染色体区域和基因关联方面的差异。这可能会导致重大的生物学发现，并有助于更好地理解疾病（如癌症）的机制及其与染色体结构和关联的关系。

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.