RUI: Using computational homology to detect DNA Copy Number Aberrations in Breast Cancer

大型复杂数据集的分析对计算数学提出了重大挑战。拓扑数据分析（TDA）应用代数拓扑的概念来应对这一挑战。拓扑技术已成功地应用于工程和生物学，但很少应用于基因组数据的分析。在癌症基因组学中，拷贝数畸变（CNA）如DNA片段的获得和丢失的鉴定是一个重要的问题，因为已知CNA含有癌症基因，因此涉及关键信号通路的错误调节。CNA可以独立发生，也可以共同发生。后者被认为是协同作用的，因此会产生不可预见的后果。例如，8 p12和11q13.3中的CNA在一些乳腺癌中共扩增的发现导致了MYC和TP 53途径之间的功能相互作用的发现。这种相互作用为癌症研究提供了一个重要的范例，因为许多肿瘤被认为使用类似的机制进行进展。传统上，共现CNA的识别受到两个因素的阻碍，一是发现共现所需的大样本量，二是缺乏有效识别它们的数学方法。最近，基于微阵列的大型数据集已可用于乳腺癌。该研究旨在开发一种新的基于TDA的方法来检测乳腺癌中独立和共同发生的CNA。在所提出的方法中，每个CNA配置文件的特征在于由一组生物学意义的拓扑空间。这些空间的拓扑不变量（即，Betti数）将用于对数据进行降噪并识别CNA。该项目将产生广泛适用的方法：（1）以适合拓扑分析的形式表示复杂数据集;（2）确定TDA结果的统计意义;（3）从大型数据集计算拓扑不变量。迫切需要新的数学方法来解决这些高维数据分析中的基本问题。在基因组学领域，已经获得了数以千计的测量结果，目的是揭示表征基本生物过程的分子特征。这一领域已显着影响了乳腺癌的研究方向，因为它的潜力，区分各种亚型，途径和疾病。目前，检测基因组签名的主要方法集中在单个独立事件的识别上。然而，越来越多的证据表明，拷贝数畸变（CNA）-如基因组的扩增和缺失-并不总是相互独立的;相反，它们可能共同发生协同和不可预见的后果。例如，在乳腺癌中检测到的共同发生的CNA导致了不同信号通路之间的串扰的鉴定。由于缺乏足够的数学方法来识别它们，系统地搜索共现的CNA受到了阻碍。PI建议开发拓扑数据分析的新方法，以识别乳腺癌中同时发生的CNA。此外，由于拷贝数变化与其他疾病和进化过程有关，该项目将对基础科学（例如进化和发展）和应用科学（例如具有遗传成分的疾病，如癌症，自闭症和多发性硬化症）产生重要影响。拟议的研究将推进数学遗传学/基因组学领域的新工具，用于分析遗传/基因组数据中遗传元素之间复杂的相互作用。所开发的方法也有可能扩展到确定在大型，复杂的纵向数据集的共同发生的事件。为了进一步扩大其更广泛的影响，该项目将举办一系列关于计算数学在现实生活中的应用的公开讲座，特别面向当地学校教师、学生和专业人员。

The analysis of large complex data sets poses a major challenge for computational mathematics. Topological Data Analysis (TDA) applies concepts from algebraic topology to address this challenge. Topological techniques have been used successfully in engineering and biology but are seldom applied to the analysis of genomic data. In cancer genomics, the identification of copy number aberrations (CNAs) such as gains and losses of DNA segments is an important problem because CNAs are known to contain cancer genes and therefore to be involved in misregulation of key signaling pathways. CNAs may occur independently or may co-occur. The latter are believed to act synergistically and therefore result in unforeseen consequences. For example, the finding that CNAs in 8p12 and 11q13.3 are co-amplified in some breast cancers led to the discovery of functional interactions between the MYC and the TP53 pathways. Such interactions offer an important paradigm for cancer research because many tumors are believed to use similar mechanisms for their progression. Identification of co-occurring CNAs has traditionally been hindered both by the large sample sizes required to find co-occurrences and by the lack of mathematical methods to identify them efficiently. Recently, large microarray-based data sets have become available for breast cancer. The proposed research aims to develop a new TDA-based method to detect independent and co-occurring CNAs in breast cancer. In the proposed approach each CNA profile is characterized by a set of biologically-meaningful topological spaces. Topological invariants of these spaces (i.e., Betti numbers) will be used to de-noise the data and identify CNAs. This project will yield broadly-applicable methods for: (1) representing complex data sets in forms that are amenable to topological analysis; (2) determining the statistical significance of TDA results; (3) computing topological invariants from large data sets.Rapid advances in the sciences have generated large, complex data sets of unprecedented proportions. New mathematical methods are urgently needed in order to solve fundamental problems in the analysis of such high-dimensional data. In the field of genomics, thousands of measurements have been obtained with the goal of unveiling molecular signatures that characterize essential biological processes. This field has significantly influenced the direction of breast cancer research because of its potential for differentiating various subtypes, pathways and prognoses of the disease. Currently, the major approach to detecting genomic signatures is focused on the identification of single independent events. However, there is increasing evidence that copy number aberrations (CNAs)-- such as amplifications and deletions of the genome--are not always independent of one another; rather, they may co-occur with synergistic and unforeseen consequences. For example, co-occurring CNAs detected in breast cancer have led to the identification of cross-talk between different signaling pathways. The systematic search for co-occurring CNAs has been hampered by a lack of mathematical methods adequate to identify them. The PI proposes to develop new methods in Topological Data Analysis to identify co-occurring CNAs in breast cancer. Further, because copy number changes are associated with other diseases and with evolutionary processes, this project will have important impacts across the sciences, both basic (e.g. evolution and development) and applied (e.g. diseases with a genetic component such as cancer, autism and multiple sclerosis). The proposed research will advance the field of mathematical genetics/genomics with new tools for analyzing complex interactions among genetic elements in genetic/genomic data. The methods developed also have the potential for extension to identify co-occurring events in large, complex longitudinal data sets. Furthering its broader impacts, the project will implement a series of public lectures on real-life applications of computational mathematics with special outreach to local school teachers, students and professionals.