Energy spectrum of the ideal DNA knot on a torus

In this study, we consider DNA as a torus knot that is formed by an elastic string. In order to determine what kinds of knot could be formed, we present its energy spectrum by combining Euler rotation, DNA's mechanical properties, and the modified Faddeev-Skyrme model. Our results theoretically demonstrated that the flexural rigidity of DNA plays an important role. If it is smaller than a critical value, DNA is likely to form a coiled structure. Conversely, above the critical value, DNA forms a twisting structure. The energy spectrum provides a way to identify the types of knots that are most likely to be created by DNA, according to the principle of energy minimisation, and with implications for its functional and packaging states in the cell nucleus.