The hopfion structure in DNA knots

DNA topology has long been a focal point of interdisciplinary research. From the White–Calugareanu formula describing double helices and supercoiling to the Hopf theory representing torus knots in DNA, researchers have extensively studied the complex topological structures of DNA. However, further research is needed to understand the relationship between DNA knot structures and their specific overall twisting and supercoiling numbers. This paper utilizes Φ-mapping topological current theory to construct Hopfions in DNA, aiming to describe torus knots in DNA. Additionally, leveraging Hopf theory, it identifies the Hopf charge as a topological invariant in DNA knots, combined with the White formula to explore the quantitative relationship between DNA topology and its structural deformations. This provides a novel perspective for investigating the topological properties of DNA.