DNA Knotting and Linking: Applications of 3-Manifold Topology to DNA-Protein Interactions

DNA 打结和连接：三流形拓扑在 DNA-蛋白质相互作用中的应用

• 批准号: EP/G039585/1
• 负责人: Dorothy Buck
• 金额: $ 41.83万
• 依托单位: Imperial College London
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2009
• 资助国家: 英国
• 起止时间: 2009 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FG039585%2F1
• 关键词: DNA; Knotting; Linking; Applications; Manifold

DNA is one of the very few parts of modern molecular biology familiar to almost everyone. We all know that DNA is responsible for our genetic inheritance and have all seen models of DNA as a two-stranded molecule with a shape like a double spiral staircase, a so-called double helix. In all the usual pictures of DNA the axis of the double helix looks nice and straight. However, in all cells the axis of any DNA molecule is far from straight and is in fact incredibly twisted up; it occupies much less space this way. Sometimes, the deviation from straight is even more pronounced. For example in bacterial cells, the two ends of a DNA molecule can be joined up to form circular DNA. If we take a piece of string and join the ends we sometimes get a knot in the string. Exactly the same thing can happen when the 2 ends of a DNA molecule get joined up and so DNA knots are born. More generally if we have two or more pieces of string and tie up the ends of all the pieces of string then we get many knots that might be linked together-like the Olympic rings. So if we have not just one but many DNA molecules then we can form DNA links as well as DNA knots.Since their discovery in the late 1960s, DNA knots and links have been found to play key roles in hosts of cellular processes. Because they are so ubiquitous all organisms have developed special proteins--topoisomerases--whose function is to help untie DNA knots and links. There are also other important proteins--called recombinases and transposes--that can alter the order of the sequence of the DNA basepairs. While the main function of recombinases and transposes is to rearrange the order of basepairs, in the process of doing this they often cause changes to DNA knotting or linking. For all these reasons molecular biologists became interested in learning about knots and links.Mathematicians have studied knots since the late 19th century for their own reasons, having nothing to do with DNA. Mathematically a knot is a one-dimensional object sitting inside 3-space, just like a standard circle does, but which we cannot smoothly deform to a standard circle. The mathematical theory of knots and links turns out to be very rich and surprisingly complicated, and intimately related to general 3-dimensional spaces, called 3-manifolds. (The study of these spaces is called 3-manifold topology.) Although the subject is very deep, some of the simplest questions remain unanswered: even today if you hand the world's top knot theorists two sufficiently complicated knots there is no known algorithm they can use to always tell whether one knot can be deformed into the other. Using tools from knot theory, mathematicians have been able to help biologists better understand the ways some proteins interact with DNA. For example, mathematicians, including the applicant, have developed models of how the recombinase and transposase proteins reshuffle the DNA sequence. These models can then predict various new features of these interactions -- e.g. particular geometric configuration the DNA takes when the protein is attached or what biochemical pathway the reactions proceeds through. DNA can form very complicated knots. But only a small fraction of all possible very complicated knots appear as DNA knots. Recently I characterized which knots can show up after a recombinase acts on an initial family of DNA knot configurations. In this proposal we will explore this question for a much wider family of initial DNA configurations, and also the analogous question for transposase reactions. We will also consider unknotting and unlinking DNA molecules. In particular we hope to understand when two DNA knots are related by a crossing change. To answer these questions, we will use cutting-edge techniques from 3-manifold topology. The answers will help us understand these important proteins, the main targets of antibiotics and some anti-cancer drugs, more completely.

DNA是现代分子生物学中几乎每个人都熟悉的少数几个部分之一。我们都知道DNA负责我们的遗传，并且都看到过DNA作为双链分子的模型，其形状像双螺旋楼梯，即所谓的双螺旋。在所有常见的DNA图片中，双螺旋的轴看起来都很好，很直。然而，在所有细胞中，任何DNA分子的轴都远非直的，事实上是令人难以置信的扭曲;它这样占据的空间要小得多。有时，偏离直线的情况甚至更加明显。例如，在细菌细胞中，DNA分子的两端可以连接起来形成环状DNA。如果我们拿一根绳子，把两端连起来，有时绳子会打结。当DNA分子的两端连接起来时，也会发生完全相同的事情，因此DNA结诞生了。更一般地说，如果我们有两条或更多的绳子，并把所有绳子的末端绑起来，那么我们就会得到许多可能连接在一起的结，就像奥林匹克五环一样。因此，如果我们有不止一个而是多个DNA分子，那么我们就可以形成DNA链和DNA结。自从20世纪60年代末发现DNA结和DNA链以来，人们发现它们在细胞过程的宿主中起着关键作用。因为它们是如此普遍，所有的生物体都发展出了特殊的蛋白质--拓扑异构酶--其功能是帮助解开DNA的结和连接。还有其他重要的蛋白质-称为重组酶和转座-可以改变DNA碱基对序列的顺序。虽然重组酶和转座酶的主要功能是重新排列碱基对的顺序，但在这样做的过程中，它们通常会导致DNA打结或连接的变化。由于所有这些原因，分子生物学家开始对研究结和连接感兴趣，数学家们从世纪末开始研究结也有自己的原因，与DNA无关。从数学上讲，一个结是一个位于三维空间中的一维物体，就像一个标准的圆一样，但我们不能平滑地变形为一个标准的圆。结和链接的数学理论非常丰富，而且令人惊讶地复杂，与一般的三维空间密切相关，称为三维流形。(The对这些空间的研究称为3-流形拓扑。虽然这个问题非常深刻，但一些最简单的问题仍然没有答案：即使在今天，如果你交给世界顶级的结理论家两个足够复杂的结，他们也没有已知的算法可以用来判断一个结是否可以变形为另一个结。利用纽结理论的工具，数学家已经能够帮助生物学家更好地理解一些蛋白质与DNA相互作用的方式。例如，包括本申请人在内的数学家已经开发出重组酶和转座酶蛋白如何重排DNA序列的模型。然后，这些模型可以预测这些相互作用的各种新特征-例如，当蛋白质附着时，DNA采取特定的几何构型，或者反应通过什么生化途径进行。DNA可以形成非常复杂的结。但在所有可能的非常复杂的结中，只有一小部分以DNA结的形式出现。最近，我描述了在重组酶作用于DNA结构型的初始家族后，哪些结可以出现。在这个建议中，我们将探讨这个问题的一个更广泛的家庭的初始DNA构型，也转座酶反应的类似问题。我们还将考虑解开和解开DNA分子。特别是，我们希望了解两个DNA结何时通过交叉变化而相关。为了回答这些问题，我们将使用来自3-流形拓扑的尖端技术。这些答案将有助于我们更全面地了解这些重要的蛋白质，这些蛋白质是抗生素和一些抗癌药物的主要靶标。

项目成果

Topological aspects of DNA function and protein folding.

DNA 功能和蛋白质折叠的拓扑方面。

• DOI: 10.1042/bst20130006
• 发表时间: 2013
• 期刊: Biochemical Society transactions
• 影响因子: 3.9
• 作者: Stasiak A

Predicting knot and catenane type of products of site-specific recombination on twist knot substrates.

预测扭结基底上位点特异性重组产物的结和索烷类型。

• DOI: 10.1016/j.jmb.2011.05.048
• 发表时间: 2011
• 期刊: Journal of molecular biology
• 影响因子: 5.6
• 作者: Valencia K

Topology and Geometry of Biopolymers

生物聚合物的拓扑和几何结构

• DOI: 10.1090/conm/746/15003
• 发表时间: 2020
• 作者: Buck D

Characterization of knots and links arising from site-specific recombination on twist knots

扭结上特定位点重组产生的结和链接的表征

• DOI: 10.1088/1751-8113/44/4/045002
• 发表时间: 2011
• 期刊: Mathematical and Theoretical
• 作者: Buck D

Connect sum of lens spaces surgeries: application to Hin recombination

连接晶状体间隙手术之和：在 Hin 重组中的应用

• DOI: 10.1017/s0305004111000090
• 发表时间: 2011
• 期刊: Mathematical Proceedings of the Cambridge Philosophical Society
• 影响因子: 0.8
• 作者: BUCK D