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

基本信息

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

项目摘要

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产生数据，通常包括及时测量基因序列信息。分子生物学的目标之一是了解生成这些数据的过程。这可以通过探索不同的假设来实现，这些假设被转化为称为模型的数学方程。我研究的主要成果将是一系列新方法来理解具有不同数据量的不同场景中的模型。该提案的重点是遗传数据。遗传水平上的分子相互作用通常涉及酶，因此可以被描述为生化反应（已知和假设的）。在 DNA 中，称为重组酶的蛋白质家族会重新排列 DNA 序列。这里的重点是位点特异性重组酶，它们只在某些位点结合 DNA。从生化角度来说，DNA 是底物，重组酶是催化变化的酶。研究DNA的数学模型要么关注DNA在核苷酸水平上的变化，要么关注整体结构。由于DNA可以被认为是一根绳子，当重组酶作用于DNA时，它也可以改变DNA的打结。局部层面的分析在数学上采用代数，而全局层面的分析则使用拓扑学（研究形状的数学领域）。通过一名在读博士生最近的工作，我们得到了初步结果，即需要将丝带类别和新理论融合到 DNA 的局部和全局视图中。该项目的目的是进一步发展数学理论和方法，开发已知位点特异性重组酶和所得 DNA 结（存在于称为拓扑异构酶的不同类别酶中）的数据库，然后创建预测软件。最终的扩展是如何考虑序列级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。理解结能量与无结有关，这涉及结理论中一个未解决的大问题：是否存在多项式时间算法来检测无结。我将开发的方法需要结合纯数学（特别是代数和拓扑）的思想）具有计算、统计和应用数学技术。将传统上不交叉的不同领域的思想和技术结合起来，对于跨学科研究和新数学思想的发展来说是一个令人兴奋的机会。我有在这个交叉点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。该项目带来的数学方法和算法的进步，与数据生成技术相结合，将使我们能够以新的方式接近和理解现实世界的生物系统。