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

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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.