RS Fellow - EPSRC grant (2016): Algebraic and topological approaches for genomic data in molecular biology

RS 研究员 - EPSRC 资助（2016）：分子生物学中基因组数据的代数和拓扑方法

• 批准号: EP/R005125/1
• 负责人: Heather Harrington
• 金额: $ 34.57万
• 依托单位: University of Oxford
• 依托单位国家: 英国
• 项目类别: Fellowship
• 财政年份: 2017
• 资助国家: 英国
• 起止时间: 2017 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FR005125%2F1
• 关键词: RS; Fellow; EPSRC; grant; 2016; RS; Fellow; EPSRC; grant; 2016

Modern science generates data at an unprecedented rate, often including the measurement of genetic sequence information in time. One aim in molecular biology is to understand the processes that generate these data; this can be achieved by exploring different hypotheses that are translated into mathematical equations called models. The main outcome of my research will be a range of new methods to understand models in different scenarios with varying amounts of data. The focus of this proposal is genetic data.The molecular interactions at the genetic level often involve enzymes and therefore can be described as biochemical reactions (known and hypothesised). In DNA, a family of proteins called recombinases rearrange DNA sequences. The focus here will be on the class of site-specific recombinases, which only bind to the DNA at certain sites. Biochemically, the DNA is the substrate and the recombinase is the enzyme that catalyses the change. The mathematical models that study DNA either focus on the changes of the DNA at the nucleotide level or the global structure. Since DNA can be thought of as a string, when a recombinase acts on the DNA, it can also change the knotting of the DNA. The local level analysis mathematically employs algebra, while the global level analysis using topology, a field of mathematics that studies shapes. With recent work by a current PhD student, we have preliminary results that ribbon categories and new theory is required to merge between the local and global view of DNA. The aim of this project is to develop the mathematical theory and methods further, develop a database of known site-specific recombinases and resulting DNA knots (which exists for a different class of enzymes called topoisomerases) and then create prediction software. Final extensions are how to take into account uncertainty/noise in either the sequence level data or the global structure experimental image data. The second part of this project is to consider how a knot's configuration relates to its energy. Understanding the knot energies relates to unknots, which relates to a large unsolved problem in knot theory: Is there a polynomial-time algorithm to detect the unknot.The methods that I will develop require marrying ideas from pure mathematics (in particular from algebra and topology) with computing, statistics, and techniques from applied mathematics. To combine ideas and techniques from different fields that traditionally do not intersect is an exciting opportunity for interdisciplinary research, and the development of new mathematical ideas. I have experience conducting research projects at this intersection, and employing new methods to gain a new understanding of biological systems. The advances in mathematical methods and algorithms that result from this project, in combination with data-generating technologies, will enable to approach and understand real-world biological systems in new ways.

现代科学以前所未有的速度生成数据，通常包括及时测量遗传序列信息。分子生物学的目标之一是了解产生这些数据的过程。这可以通过探索转化为称为模型的数学方程式的不同假设来实现。我的研究的主要结果将是一系列新方法，可以在不同的情况下了解不同情况下的模型。该建议的重点是遗传数据。遗传水平的分子相互作用通常涉及酶，因此可以描述为生化反应（已知和假设）。在DNA中，一个称为重组酶重排的DNA序列的蛋白质家族。这里的重点将放在位点特异性重聚物酶的类别上，这些重点酶仅与某些位点的DNA结合。从生化上，DNA是底物，重组酶是催化变化的酶。研究DNA的数学模型要么集中于核苷酸水平上的DNA的变化或全局结构。由于可以将DNA视为串，因此重组酶作用于DNA，也可以改变DNA的打结。本地级分析在数学上采用代数，而全球级别分析使用拓扑，这是研究塑造的数学领域。随着当前一名博士生的最新工作，我们有初步的结果，即在DNA的本地和全球视图之间融合了色带类别和新理论。该项目的目的是进一步开发数学理论和方法，开发一个已知位点特异性重组酶的数据库以及由此产生的DNA结（用于不同类别称为拓扑异构酶的不同类别的酶），然后创建预测软件。最终扩展是如何考虑序列级别数据或全局结构实验图像数据中的不确定性/噪声。该项目的第二部分是考虑结的配置与其能量的关系。了解结与未结的关系有关，这与结理论中的一个大尚未解决的问题有关：是否存在多项式时间算法来检测未结的算法。我将开发的方法需要从纯数学（尤其是代数和拓扑结构）中与计算，统计学，统计数据和技术中的技术来结婚的想法。将传统上不相交的不同领域的思想和技术结合在一起，是跨学科研究的激动人心的机会，以及新的数学思想的发展。我有在此交叉路口进行研究项目的经验，并采用新方法来获得对生物系统的新理解。该项目与数据生成技术相结合的数学方法和算法的进步将使能够以新的方式接近并理解现实世界的生物系统。