The Dynamic Genome: Studying the Interplay between Local Strand-Passage and Reconnection

从微观的DNA重组到流体湍流中漩涡的大规模重联，再到太阳日冕环的磁重联，重联过程出现在各种不同尺度的环境中。实验数据表明，通过重组新复制的环状DNA质粒的拓扑简化途径与相互连接的流体漩涡中的拓扑简化途径有着惊人的相似性，从而指出了通过局部重新连接解除连接的普遍过程。对拓扑简化的驱动在自然界是普遍存在的，这项工作将发展对其背后规律的数学理解。诸如拓扑异构酶和重组酶之类的酶是能够简化环状DNA拓扑结构的DNA结合蛋白。它们通过局部交叉变化和局部重连接起作用。本项目的主要目的是利用结理论、低维拓扑和计算机模拟来表征DNA拓扑简化的拓扑机制。为了实现这一研究目标，中心假设是在正常条件下拓扑异构酶和重组酶遵循DNA解结和解联的最佳拓扑途径。首席研究员将通过两个具体目标来检验这一假设。(1)利用低维拓扑技术，寻找II型拓扑异构酶和重组酶解结和解联DNA的可能拓扑途径。(2)通过符号交叉变化和局部重连进行DNA拓扑简化的计算机模拟，探索与基因组结构的联系。PI和她的小组将参与各种传播和外展活动，并致力于增加数学科学的多样性。该研究将为DNA局部重连接和符号交叉变化的解结和解联建立严格的数学模型，这将有助于我们理解拓扑异构酶和重组酶的解结和解联机制。酶的作用可以建模为局部交叉变化，并作为相干或非相干带手术，分别。假设手性酶作用，该项目将研究符号交叉变化，并表征可以通过单一类型的交叉变化解开的结。不同的最小多步重连路径将在给定的结点或链接对之间确定。本研究将扩展结理论中有关交叉点变化的表征和保留拓扑结型的非相干带手术的无规律交叉点猜想和类似开放问题的研究成果。拟议的项目将开发一个计算机模型（多重马尔可夫链蒙特卡罗算法），其中反向重复位点的DNA重组被建模为非相干带手术。首席研究员将计算最小重组路径，并评估这种形式的拓扑简化在不同几何和拓扑滤波器下的效率。通过模拟，该研究将确定每种方法的转移概率网络，并选择用于标记杂交变化和DNA重组的模型的参数。这将提供节点的排名，并确定具有高连接性的拓扑类型。一个重要的重点是放在相互作用的链通道和重新连接事件。

Reconnection processes appear in a variety of settings at widely different scales, from microscopic DNA recombination to large-scale reconnection of vortices in fluid turbulence and magnetic reconnection of solar coronal loops. Experimental data show striking similarities between the pathways of topology simplification in newly replicated circular DNA plasmids by recombination and those in interlinked fluid vortices thus pointing to a universal process of unlinking by local reconnection. A drive toward topological simplification is ubiquitous in nature and this work will develop a mathematical understanding of the laws underlying it. Enzymes such as topoisomerases and recombinases are DNA-binding proteins able simplify the topology of circular DNA. They act by local crossing changes and local reconnection. The main objective of this project is to characterize the topological mechanism of DNA topology simplification using knot theory, low-dimensional topology and computer simulations. In pursuit of this research objective, the central hypothesis is that under normal conditions topoisomerases and recombinases follow optimal topological pathways of DNA unknotting and unlinking. The principal investigator will test this hypothesis through two specific aims. (1) Use techniques from low-dimensional topology, to find possible topological pathways of DNA unknotting and unlinking by type II topoisomerases and by recombinases. (2) Conduct computer simulations of DNA topology simplification by signed crossing changes and by local reconnection and explore connections to genome architecture. The PI and her group will be involved in a variety of dissemination and outreach activities, and are committed to increasing diversity in the Mathematical Sciences. The research will produce rigorous mathematical models for DNA unknotting and unlinking by local reconnection and signed crossing change, which will contribute to our understanding of the unknotting and unlinking mechanisms by topoisomerases and by recombinases. The enzymatic action can be modeled as local crossing changes, and as coherent or non-coherent band surgery, respectively. Assuming a chiral enzymatic action, this project will study signed crossing changes and characterize knots that can be unknotted with a single type of crossing change. Different minimal multi-step reconnection pathways will be identified between given pairs of knots or links. The research will extend results related to the nugatory crossing conjecture and analogous open questions in knot theory, which concerns the characterization of crossing changes and non-coherent band surgeries, which preserve the topological knot type. The proposed project will develop a computer model (a multiple Markov chain Monte Carlo algorithm) where DNA recombination at inversely repeated sites is modeled as non-coherent band surgery. The principal investigator will compute minimal recombination pathways and assess the efficiency of this form of topology simplification under different geometric and topological filters. Via simulations, the research will determine the transition probability networks for each method and choice of parameters for the models developed for signed crossing change and recombination of DNA. This will provide a ranking of the nodes and identify topology types with high-connectivity. An important focus is placed on the interplay of strand-passage and reconnection events.