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Abstract The three dimensional organization of genomes remains mostly unknown due to their high degree of condensation. Biophysical studies predict that condensation promotes the topological entanglement of chromatin fibers and the inhibition of function. How organisms balance between functionally active genomes and a high degree of condensation remains to be determined. Here we hypothesize that the Rabl configuration, characterized by the attachment of centromeres and telomeres to the nuclear envelope, helps to reduce the topological entanglement of chromosomes. To test this hypothesis we developed a novel method to quantify chromosome entanglement complexity in 3D reconstructions obtained from Chromosome Conformation Capture (CCC) data. Applying this method to published data of the yeast genome, we show that computational models implementing the attachment of telomeres or centromeres alone are not sufficient to obtain the reduced entanglement complexity observed in 3D reconstructions. It is only when the centromeres and telomeres are attached to the nuclear envelope (i.e. the Rabl configuration) that the complexity of entanglement of the genome is comparable to that of the 3D reconstructions. We therefore suggest that the Rabl configuration is an essential player in the simplification of the entanglement of chromatin fibers. 

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. 

Site-specific recombination is an enzymatic process where two sites of precise sequence and orientation along a circle come together, are cleaved, and the ends are recombined. Site-specific recombination on a knotted substrate produces another knot or a two-component link depending on the relative orientation of the sites prior to recombination. Mathematically, site-specific recombination is modeled as coherent (knot to link) or non-coherent (knot to knot) banding. We here survey recent developments in the study of non-coherent bandings on knots and discuss biological implications.