Title:  Mathematical models to study RNA interactions with DNA
Abstract:  We focus on some non-standard roles of transcript RNA that can be modeled with discrete mathematical methods such as graphs, words (Gauss codes) and formal grammars. RNA templated DNA recombination has been observed during development of somatic nuclei in some species of ciliates. We show DNA recombination models based on 4-regular graphs and Gauss codes. Formation of co-transcriptional transient three-stranded nucleic acids that form during transcription are RNA-DNA hybrids, also known as R-loops, form when the nascent RNA hybridizes to the template DNA, freeing the DNA coding strand. We show a formal grammar model approach to modeling R-loops. Although the model has no explicit topological information, the R-loop grammar seems to predict R-loop formation on plasmids with varying starting topologies.