R-loops are abundant three-stranded nucleic-acid structures that formin cisduring transcription. Experimental evidence suggests that R-loop formation is affected by DNA sequence and topology. However, the exact manner by which these factors interact to determine R-loop susceptibility is unclear. To investigate this, we developed a statistical mechanical equilibrium model of R-loop formation in superhelical DNA. In this model, the energy involved in forming an R-loop includes four terms—junctional and base-pairing energies and energies associated with superhelicity and with the torsional winding of the displaced DNA single strand around the RNA:DNA hybrid. This model shows that the significant energy barrier imposed by the formation of junctions can be overcome in two ways. First, base-pairing energy can favor RNA:DNA over DNA:DNA duplexes in favorable sequences. Second, R-loops, by absorbing negative superhelicity, partially or fully relax the rest of the DNA domain, thereby returning it to a lower energy state. In vitro transcription assays confirmed that R-loops cause plasmid relaxation and that negative superhelicity is required for R-loops to form, even in a favorable region. Single-molecule R-loop footprinting following in vitro transcription showed a strong agreement between theoretical predictions and experimental mapping of stable R-loop positions and further revealed the impact of DNA topology on the R-loop distribution landscape. Our results clarify the interplay between base sequence and DNA superhelicity in controlling R-loop stability. They also reveal R-loops as powerful and reversible topology sinks that cells may use to nonenzymatically relieve superhelical stress during transcription.

In Escherichia coli DNA replication yields interlinked chromosomes. Controlling topological changes associated with replication and returning the newly replicated chromosomes to an unlinked monomeric state is essential to cell survival. In the absence of the topoisomerase topoIV, the site-specific recombination complex XerCD- dif-FtsK can remove replication links by local reconnection. We previously showed mathematically that there is a unique minimal pathway of unlinking replication links by reconnection while stepwise reducing the topological complexity. However, the possibility that reconnection preserves or increases topological complexity is biologically plausible. In this case, are there other unlinking pathways? Which is the most probable? We consider these questions in an analytical and numerical study of minimal unlinking pathways. We use a Markov Chain Monte Carlo algorithm with Multiple Markov Chain sampling to model local reconnection on 491 different substrate topologies, 166 knots and 325 links, and distinguish between pathways connecting a total of 881 different topologies. We conclude that the minimal pathway of unlinking replication links that was found under more stringent assumptions is the most probable. We also present exact results on unlinking a 6-crossing replication link. These results point to a general process of topology simplification by local reconnection, with applications going beyond DNA.

Understanding the folding of the human genome is a key challenge of modern structural biology. The emergence of chromatin conformation capture assays (e.g., Hi-C) has revolutionized chromosome biology and provided new insights into the three dimensional structure of the genome. The experimental data are highly complex and need to be analyzed with quantitative tools. It has been argued that the data obtained from Hi-C assays are consistent with a fractal organization of the genome. A key characteristic of the fractal globule is the lack of topological complexity (knotting or inter-linking). However, the absence of topological complexity contradicts results from polymer physics showing that the entanglement of long linear polymers in a confined volume increases rapidly with the length and with decreasing volume. In vivo and in vitro assays support this claim in some biological systems. We simulate knotted lattice polygons confined inside a sphere and demonstrate that their contact frequencies agree with the human Hi-C data. We conclude that the topological complexity of the human genome cannot be inferred from current Hi-C data.

In Escherichia coli DNA replication yields interlinked chromosomes. Controlling topological changes associated with replication and returning the newly replicated chromosomes to an unlinked monomeric state is essential to cell survival. In the absence of the topoisomerase topoIV, the sitespecific recombination complex XerCD-dif-FtsK can remove replication links by local reconnection. We previously showed mathematically that there is a unique minimal pathway of unlinking replication links by reconnection while stepwise reducing the topological complexity. However, the possibility that reconnection preserves or increases topological complexity is biologically plausible. In this case, are there other unlinking pathways? Which is the most probable? We consider these questions in an analytical and numerical study of minimal unlinking pathways. We use a Markov Chain Monte Carlo algorithm with Multiple Markov Chain sampling to model local reconnection on 491 different substrate topologies, 166 knots and 325 links, and distinguish between pathways connecting a total of 881 different topologies. We conclude that the minimal pathway of unlinking replication links that was found under more stringent assumptions is the most probable. We also present exact results on unlinking a 6-crossing replication link. These results point to a general process of topology simplification by local reconnection, with applications going beyond DNA.Flexible circular chains appear often in nature, from microscopic DNA plasmids to macroscopic loops in solar corona. Such chains entrap rich geometrical and topological complexity which can give insight into the processes underlying their formation or modification. Knotted and interlinked states often coincide with higher energy states in physical systems and are usually undesired. Topology-simplifying reconnection processes involving one or two cleavages are observed. Examples in biology include the action of type II topoisomerases and of site-specific recombinases. Type II topoisomerases bind to two segments of double-stranded DNA, cleave one of the segments, transport the other through the break (strand-passage) and reseal the break. Site-specific recombinases bind to two specific sites (short segments of double-stranded DNA), introduce a double-stranded break on each site, recombine the ends and reseal the breaks. The action of recombination enzymes is a local reconnection event. We here investigate pathways of unlinking of newly replicated DNA links by local reconnection. The results presented, and the numerical methods proposed are not restricted to the biological example and are applicable to any local reconnection process.In genetics, the observation of topological links dates back to studies in plants in the 1930s. In a study of chromosomal variation in Crepis tectorum, M. Navashin observed ring chromosomes, noting "in one case, the two daughter strands composing a normal chromosome failed to separate". Navashin reported on a metaphase involving four rings, two of which were "united in the...