The Dynamic Genome: Studying the Interplay between Local Strand-Passage and Reconnection

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Reconnection processes appear in a variety of settings at widely different scales, from microscopic DNA recombination to large-scale reconnection of vortices in fluid turbulence and magnetic reconnection of solar coronal loops. Experimental data show striking similarities between the pathways of topology simplification in newly replicated circular DNA plasmids by recombination and those in interlinked fluid vortices thus pointing to a universal process of unlinking by local reconnection. A drive toward topological simplification is ubiquitous in nature and this work will develop a mathematical understanding of the laws underlying it. Enzymes such as topoisomerases and recombinases are DNA-binding proteins able simplify the topology of circular DNA. They act by local crossing changes and local reconnection. The main objective of this project is to characterize the topological mechanism of DNA topology simplification using knot theory, low-dimensional topology and computer simulations. In pursuit of this research objective, the central hypothesis is that under normal conditions topoisomerases and recombinases follow optimal topological pathways of DNA unknotting and unlinking. The principal investigator will test this hypothesis through two specific aims. (1) Use techniques from low-dimensional topology, to find possible topological pathways of DNA unknotting and unlinking by type II topoisomerases and by recombinases. (2) Conduct computer simulations of DNA topology simplification by signed crossing changes and by local reconnection and explore connections to genome architecture. The PI and her group will be involved in a variety of dissemination and outreach activities, and are committed to increasing diversity in the Mathematical Sciences. The research will produce rigorous mathematical models for DNA unknotting and unlinking by local reconnection and signed crossing change, which will contribute to our understanding of the unknotting and unlinking mechanisms by topoisomerases and by recombinases. The enzymatic action can be modeled as local crossing changes, and as coherent or non-coherent band surgery, respectively. Assuming a chiral enzymatic action, this project will study signed crossing changes and characterize knots that can be unknotted with a single type of crossing change. Different minimal multi-step reconnection pathways will be identified between given pairs of knots or links. The research will extend results related to the nugatory crossing conjecture and analogous open questions in knot theory, which concerns the characterization of crossing changes and non-coherent band surgeries, which preserve the topological knot type. The proposed project will develop a computer model (a multiple Markov chain Monte Carlo algorithm) where DNA recombination at inversely repeated sites is modeled as non-coherent band surgery. The principal investigator will compute minimal recombination pathways and assess the efficiency of this form of topology simplification under different geometric and topological filters. Via simulations, the research will determine the transition probability networks for each method and choice of parameters for the models developed for signed crossing change and recombination of DNA. This will provide a ranking of the nodes and identify topology types with high-connectivity. An important focus is placed on the interplay of strand-passage and reconnection events.