Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2015, Director: Carles CasacubertaSome enzymes like condensins or type II topoisomerases are capable of changing the topology of cyclic DNA molecules. The first ones introduce positive superhelical tension into double-stranded DNA and the second ones perform strand passages that cut both strands of one DNA double helix, pass another unbroken DNA helix through it, and then religate the cut strands. Motivated by the action of topoisomerases in knotted DNA, we study transition probabilities between knot diagrams and compute stationary distributions of the strand-passage Markov process. First we give a brief introduction to knot theory, braid theory and random processes, particularly to Markov chains. After this, we propose a new model for strand passage in knot diagrams based on Artin’s braid group. This braid-based model allows us to generate a large set of braid diagrams with which we are able to simulate the action of type II topoisomerases
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