# Yannan Shen

## Mathematical analysis of DNA unknotting by type II topiosomerases

Type II topoisomerases are enzymes that can change the topology of circular DNA molecules. These enzymes are essential to every living organism, which makes them good targets for anti-cancer and anti-bacterial drugs. DNA topology assays are used to determine the efficiency of topoisomerase inhibitors in drug design. In my research, I focus on the unknotting probability of knots by type II topoisomerases. In our previous study, our group built a mathematical model in simple cubic lattice to simulate how random strand passages generate the knotting distribution. We intended to use a sophisticated theoretical framework and efficient computer simulations to test and compare some of the existing models and propose new ones. I aim to implement the random strand-passage model in the Dowker code level to discover how topo II simplifies knots under the thermal dynamic equilibrium level.

### Message to Sponsor

**Major:**Mathematics**Mentor:**Rainer Sachs, Mathematics