DMS/NIGMS 2: Collaborative Research: Modeling R-Loop Formation and Topology Using Braids and Graphs Coupled with Single-Molecule Footprinting

生命的两个姊妹分子，RNA和DNA的相互作用，长期以来一直是科学探究的焦点。最近发现了一种新的分子复合物，称为r环，由DNA双链和RNA链组成。已经发现r环是普遍存在的，并且被证明是在从细菌到哺乳动物的整个生命王国中观察到的功能重要的结构。r环现在被认为是一种新型的信号，在越来越多的生物过程中起着重要的作用。r环形成缺陷与包括人类在内的多种物种的疾病有关。然而，目前对r -环的形成和结构了解甚少。该项目将解决控制r -环起始的力量，r -环开始和终止的方式，RNA-DNA复合物的几何形状，以及决定r -环稳定性的因素。这项工作将推动数学和生物学领域的发展，同时通过将理论方法与实验工作相结合，加强它们之间的相互联系。该研究为实验和数学生物学的博士后、研究生和本科生培训提供了新的途径，并包括专门由女数学家和为女数学家提供的指导部分，以支持她们参与科学并提高她们的知名度。研究结果将广泛传播。r环是由RNA、DNA双链和DNA单链组成的三链结构。r环最初发现于细菌中，占酵母、植物和哺乳动物基因组的3-5%。该项目使用新颖的数学方法来检查DNA序列和DNA拓扑结构对r环形成的影响，并探索r环的三维几何形状。本项目的目标是通过实现以下三个具体目标，阐明引导r -环的起始、延伸、终止和最终解离的序列以及拓扑和空间约束：(1)通过实验剖析DNA序列对r -环形成的影响，并利用这些发现开发辫语法来模拟和预测r -环的外观；(2)揭示DNA拓扑结构在调控r环形成中的作用，并描述其三维结构；(3)发展基于编织语法和有向图的数学技术，探索r环形成的动态。除了解决关键的生物学问题外，这项工作还将产生新的数学知识，并有助于跨学科研究新兴领域的发展。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

Interactions of the two sister molecules of life, RNA and DNA, have long been a focus of scientific inquiry. A new molecular complex, known as an R-loop, consisting of a DNA duplex and an RNA strand was recently discovered. It has been found that R-loops are prevalent, and shown to be functionally important structures that are observed across the kingdom of life, from bacteria to mammals. R-loops are now understood to act as a new type of signal with important roles in a growing number of biological processes. Defects in R-loop formation have been implicated in disease in a wide variety of species including humans. However, little is currently understood about the formation and the structure of R-loops. This project will address the forces that control R-loop initiation, the way in which R-loops start and terminate, the geometry of the RNA-DNA complex, and the factors that dictate R-loop stability. This work will advance the fields of mathematics and biology while also reinforcing their mutual interconnections through blending theoretical approaches with experimental work. The research provides new avenues for postdoctoral, graduate and undergraduate training in experimental and mathematical biology and includes a mentoring component specifically by and for women mathematicians to support their scientific engagement and increase their visibility. The research findings will be disseminated broadly. R-loops are three-stranded structures composed of an RNA:DNA duplex and a single-strand of DNA. Initially found in bacteria, R-loops can account for 3-5% of the genome of yeasts, plants and mammals. This project uses novel mathematical approaches to examine the effects of DNA sequence and DNA topology on R-loop formation and to probe the three-dimensional geometry of R-loops. The goal of this project is to elucidate the sequence and the topological and spatial constraints that guide the initiation, elongation, termination, and ultimate dissociation of R-loops, through implementing the following three specific aims: (1) Experimentally dissect the influence of DNA sequence on R-loop formation and use these findings to develop braid grammars that model and predict the appearance of R-loops; (2) Uncover the role of DNA topology in regulating the formation of R-loops, and describe their 3D structure; and (3) Develop mathematical techniques based on braid grammars and directed graphs that probe the dynamics of R-loop formation. In addition to addressing key biological questions, the work will generate new mathematical knowledge and contribute to the development of an emergent area of interdisciplinary study.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.