III: Small: Models and Methods for Simultaneous Genotyping and Phylogeny Inference from Single-Cell DNA Data

癌症是一种由体细胞组织中的单个细胞产生的疾病，由体细胞突变、拷贝数异常和染色体重排的复杂相互作用所驱动。随着肿瘤的进展，不同的基因组异常会产生遗传上不同的细胞亚群(克隆)，这些细胞在达尔文式的突变、适应和选择框架中相互作用。肿瘤内异质性(ITH)使癌症患者的诊断和治疗复杂化，并导致复发和耐药。下一代测序(NGS)技术的出现使得通过产生大规模的定量基因组数据集来彻底分析肿瘤的异质性成为可能。然而，尽管取得了这些进展，到目前为止，对肿瘤内异质性的全面了解仍然是难以捉摸的。该项目需要设计新的数学公式和开发新的算法技术来推断肿瘤细胞的进化史，以了解肿瘤的演变和ITH。特别是，所有的模型和方法都以单细胞测序(SCS)数据为目标，同时考虑了变异调用和基因分型，以及进化历史推断。这一同时推论以原则性的方式解释了SCS数据中的错误。基于有限和无限场地假设的模型将被推导出来。这项研究是高度跨学科的，使用组合优化和图论以及统计估计，为癌症基因组学中出现的问题提供实用的解决方案。虽然该项目的主要影响将是癌症生物学，但该项目也将刺激数学、计算机科学和统计学交叉领域的研究。该项目将在真正跨学科的环境中为学生提供培训机会。该项目将生产免费提供的开源软件。研究成果将纳入课程并通过出版物传播。所有模型和算法将在开源软件中实现，并通过Github和BitBucket传播。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

Cancer is a disease that emerges from a single cell in the somatic tissue and is driven by a complex interplay of somatic mutations, copy number aberrations and chromosomal rearrangements. As a tumor progresses, diverse genomic aberrations give rise to genetically heterogeneous subpopulations (clones) of cells that interact with each other in a Darwinian framework of mutations, fitness and selection. Intra-tumor heterogeneity (ITH) complicates the diagnosis and treatment of cancer patients and causes relapse and drug resistance. The emergence of next-generation sequencing (NGS) technologies has enabled a thorough analysis of tumor heterogeneity through the generation of large-scale quantitative genomic datasets. However, despite these advances, a comprehensive understanding of intra-tumor heterogeneity has proved elusive thus far.The project entails devising new mathematical formulations and developing new algorithmic techniques for inferring evolutionary histories of tumor cells in order to understand tumor evolution and ITH. In particular, all the models and methods target single-cell sequencing (SCS) data and account simultaneously for variant calling and genotyping, as well as evolutionary history inference. This simultaneous inference accounts in a principled manner for error in SCS data. Models based on both finite- and infinite-sites assumptions will be derived. The research is highly interdisciplinary, using combinatorial optimization and graph theory, as well as statistical estimation, to provide practical solutions to problems that arise in cancer genomics. While a major impact of the project will be on cancer biology, the project will also stimulate research at the intersection of mathematics, computer science and statistics. The project will provide training opportunities for students in a truly interdisciplinary setting. The project will produce freely available open-source software. The research results will be integrated into courses and disseminated through publications. All models and algorithms will be implemented in open-source software, and disseminated via Github and Bitbucket.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.