Type II topoisomerases are essential enzymes that change the topology of DNA by modifying its supercoiling, knotting, or catenation levels. Such changes are required during important cellular processes such as transcription and replication; hence, topoisomerase inhibitors are used as a drug target in antibacterial and anticancer therapies. The molecular mechanism of type II topoisomerases has been well established: the enzyme introduces a double-stranded DNA break and allows passage of one DNA segment through another. However, it is not understood how topoisomerases select the location of strand-passage such that it is able to unknot and decatenate DNA more efficiently than would be expected by unbiased random strand passage. In this study, we aim to model random strand passage on circular DNA using mathematical and computational methods. Circular DNA is modeled as a polygonal chain of fixed length in the simple cubic lattice (Z3). Each unit length in the cubic lattice represents the effective helical diameter of DNA, and, hence, each segment of the polygonal chain is scaled to represent an appropriate number of nucleic acid base pairs. Then, using Monte Carlo methods, we mimic the movement of DNA in solution by sampling numerous geometric configurations of the original polygonal chain. Lastly, using mathematical knot theory and computational methods, the three-dimensional configurations are converted into one-dimensional representations of each DNA knot and strand passage is performed. Our results show the distribution of knot types that are obtained following repeated strand passage. We conclude that our simulations are a computationally efficient way of modeling random strand passage on short DNA chains. In future work, we will discuss how to extend our model to longer DNA chains and how to overcome the limitations of working on the simple cubic lattice. We will also introduce topologic biases to the simulation to represent how type II topoisomerase unknotting behavior deviates from the random strand-passage model.
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