Creation of electrical knots and observation of DNA topology

Knots are fascinating topological structures that have been observed in various contexts, ranging from micro-worlds to macro-systems, and are conjectured to play a fundamental role in their respective fields. In order to characterize their physical properties, some topological invariants have been introduced, such as unknotting number, bridge number, Jones polynomial and so on. While these invariants have been proven to theoretically describe the topological properties of knots, they have remained unexplored experimentally because of the difficulty associated with control. Herein, we report the creation of isolated electrical knots based on discrete distributions of impedances in electric circuits and observation of the unknotting number for the first time. Furthermore, DNA structure transitions under the action of enzymes were studied experimentally using electrical circuits, and the topological equivalence of DNA double strands was demonstrated. As the first experiment on the creation of electrical knots in real space, our work opens up the exciting possibility of exploring topological properties of DNA and some molecular strands using electric circuits.