DNA Topoisomerase-Mediated Formation of DNA Olympic Gel: Kinetics of Catenation, Topological and Mechanical Properties

We simulate and investigate the kinetics of the formation of the Olympic hydrogel and the key controlling factors that may influence the catenation reaction. We find this catenation reaction of DNA rings is highly analogous to the stepwise polymerization of the polymer chain. In the catenation reaction of small DNA ring sizes, the number fraction distribution can always fit well with the Flory distribution. The gelation point of the Olympic hydrogel is possible to predict by the critical conversion of loop generation during the catenation reaction. Based on the phase diagram of the variations of catenation index and order parameter, we conclude that for the successful formation of Olympic gel by interlocked DNA rings, a sufficiently large DNA ring size and a sufficiently high initial ring concentration are both required. We also prove that the catenation index and the order parameter are solely determined by the concentration of the ring relative to its inherent overlap concentration, i.e., c0/c*. For the mechanical properties of the Olympic hydrogel, we find with the increase of the order parameter, the Olympic hydrogel shows a decrease of fracture elongation but an increase of strength. This study may help for better understanding the kinetics in the formation of the Olympic hydrogel and for the rational design and regulation of new Olympic hydrogel materials.