Even such a simple operation as connecting two ends of a linear polymer strand, thereby turning it into a ring, can have drastic impact on its properties. In contrast to the open-ended linear architecture, ring topology allows (i) linking several rings into chains, (ii) threading of the ring by other object like an eye of a needle, (iii) or tying permanent molecular knots. It is not a coincidence, that biomacromolecules such as plasmids DNA or mitochondrial DNA are ring-shaped, as this unique topology brings about extraordinary means of their bioregulation.

❓ How does the ring topology of polymer affect its properties? Are the ring polymers fluid-like or solid-like? How do they behave in flows? Do they form glasses?
❓ How do the rings respond to internal stimuli and fields? Can we open or close the interior of the ring by change of pH or temperature? Can we harvest this in smart materials?

Understanding organization of DNA inside and outside of the cell nuclei poses one of the most active open problems in biophysics. While the principles of base-pairing and sequence-specific design is well established in both living matter and DNA nanotechnology, geometrical and topological aspects of DNA polymer strands are still poorly understood. How do the topological constraints affect the structure of DNA and how is the structure regulated by enzymes such as topoisomerases or gyrases?

❓ What is the shape and size of DNA rings in solutions and in melts? Under what conditions do they self-assemble or cluster?
❓ How can we regulate twist and writhe of DNA molecules? How does supercoiling affect the properties of DNA materials?