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R-loops are nucleic acid structures consisting of a DNA:RNA hybrid and a DNA single strand. They form naturally during transcription when the nascent RNA hybridizes to the template DNA, forcing the coding DNA strand to wrap around the RNA:DNA duplex. Although formation of R-loops can have deleterious effects on genome integrity, there is evidence of their role as potential regulators of gene expression and DNA repair. Here we initiate an abstract model based on formal grammars to describe RNA:DNA interactions and the formation of R-loops. Separately we use a sliding window approach that accounts for properties of the DNA nucleotide sequence, such as C-richness and CG-skew, to identify segments favoring R-loops. We evaluate these properties on two DNA plasmids that are known to form R-loops and compare results with a recent energetics model from the Chédin Lab. Our abstract approach for R-loops is an initial step toward a more sophisticated framework which can take into account the effect of DNA topology on R-loop formation. 

R-loops are nucleic acid structures consisting of a DNA:RNA hybrid and a DNA single strand. They form naturally during transcription when the nascent RNA hybridizes to the template DNA, forcing the coding DNA strand to wrap around the RNA:DNA duplex. Although formation of R-loops can have deleterious effects on genome integrity, there is evidence of their role as potential regulators of gene expression and DNA repair. Here we initiate an abstract model based on formal grammars to describe RNA:DNA interactions and the formation of R-loops. Separately we use a sliding window approach that accounts for properties of the DNA nucleotide sequence, such as C-richness and CG-skew, to identify segments favoring R-loops. We evaluate these properties on two DNA plasmids that are known to form R-loops and compare results with a recent energetics model from the Chédin Lab. Our abstract approach for R-loops is an initial step toward a more sophisticated framework which can take into account the effect of DNA topology on R-loop formation. 

We initiate an algebraic approach to study DNA origami structures. We identify two types of basic building blocks and describe a DNA origami structure by their composition. These building blocks are taken as generators of a monoid, called the origami monoid, and motivated by the well studied Temperley-Lieb algebras, we identify a set of relations that characterize the origami monoid. We present several observations about Green’s relations for the origami monoid and study the relations to a direct product of Jones monoids, which is a morphic image of an origami monoid.