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是几乎每个人都熟悉的现代分子生物学的极少数部分之一。我们都知道，DNA负责我们的遗传遗传，并且都将DNA的模型视为具有双螺旋楼梯（所谓的双螺旋）形状的两链分子。在所有通常的DNA图片中，双螺旋的轴看起来不错且直。然而，在所有细胞中，任何DNA分子的轴都远非笔直，实际上是令人难以置信的扭曲。以这种方式占用的空间要少得多。有时，与直的偏差更加明显。例如，在细菌细胞中，可以将DNA分子的两端连接起来形成圆形DNA。如果我们拿一块绳子并连接末端，我们有时会在绳子中结成一个结。当DNA分子的两个末端结合在一起时，可能会发生同样的事情，因此DNA结出生。更一般而言，如果我们有两根或更多块绳子并绑住所有绳子的末端，那么我们会得到许多可能将类似于奥运会的打结。因此，如果我们不仅有一个而是许多DNA分子，那么我们就可以形成DNA链接以及DNA结。在1960年代后期发现的DNA结和DNA结和链接在细胞过程的宿主中起着关键作用。因为它们无处不在，所有生物都开发了特殊的蛋白质（topoisomerases），所以功能是帮助解开DNA结和链接。还有其他重要的蛋白质 - 称为重物组织酶和转置 - 可以改变DNA基底序列的顺序。虽然重组酶和转置的主要功能是重新排列基础底座的顺序，但在此过程中，它们通常会导致DNA打结或链接的变化。由于所有这些原因，分子生物学家对学习结和链接的兴趣感兴趣。自19世纪后期以来，数学家出于自己的原因进行了结，与DNA无关。从数学上讲，一个结是一个坐在3空间内部的一维对象，就像标准圆一样，但是我们无法将其平滑地变形到标准圆。结和链接的数学理论证明非常丰富且令人惊讶地复杂，并且与一般的三维空间密切相关，称为3个manifolds。 （对这些空间的研究称为3型拓扑。）尽管该主题非常深入，但一些最简单的问题仍然没有得到解答：即使在今天，如果您将世界顶级结理论家递给两个足够复杂的结两个，那么他们都无法使用一个已知的算法来始终告诉一个结的算法。使用结理论的工具，数学家已经能够帮助生物学家更好地了解某些蛋白质与DNA相互作用的方式。例如，包括申请人在内的数学家已经开发了重组酶和转座酶蛋白如何改组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功能，例如当蛋白质附着或反应通过的生化途径时，DNA采取的特定几何构型会采用。 DNA会形成非常复杂的结。但是，只有一小部分可能非常复杂的结出是DNA结。最近，我表征了重组酶作用于最初的DNA结构型家族后，哪些结可以出现。在此提案中，我们将探索这个问题，以探索更广泛的初始DNA构型家族，也是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何时通过交叉变化相关的两个DNA结。为了回答这些问题，我们将使用3个Manifold拓扑的尖端技术。这些答案将帮助我们了解这些重要的蛋白质，抗生素的主要靶标和一些抗癌药物。

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