You cannot deform a doughnut into a football, for instance. It is a different topology because of the hole. You have to cut and glue some things in order to go from a doughnut to a ball.
How does DNA topology affect living cells?
DNA topology, more specifically, is the study of the topological properties of DNA — and it is really fascinating.
Professor of Biomaterials
10 Oct 2025
Key Points
- DNA topology refers to the structural features of DNA — supercoiling, knotting and linking — that affect its function and are preserved under continuous deformation.
- Topoisomerases are essential enzymes that cut, rearrange and reseal DNA strands to manage topological problems, making them critical for processes like gene expression and cell division.
- Drugs that target DNA topology, such as antibiotics and cancer therapies, work by inhibiting topoisomerases, but they often affect both healthy and diseased cells.
- DNA topology is not inherently harmful; complex structures like knots and links may offer evolutionary or functional advantages in packaging or preserving genetic material.
Topology defined
Topology is a branch of mathematics that studies the properties of spaces that are invariant under continuous deformation, so sometimes it is called rubber sheet geometry in the sense that it is the study of spaces that you can deform as if it were a rubber sheet. You cannot cut or glue, however. To give you an example, there is a very famous joke in mathematics that you can deform a doughnut into a mug. Mathematicians sometimes get confused as to whether you have to put the doughnut into the mug or the mug into the doughnut — topologists in particular.
© Keenan Crane and Henry Segerman
Cellular DNA topology
DNA topology, more specifically, is the study of the topological properties of DNA. It is really fascinating. There are three main topological objects that are formed by DNA. The first one that is a little bit more complex to understand is supercoiling.
© Steven Lek
Because DNA is a double helix, you can imagine tightening the helix a little bit more or releasing the helix. It is a right-handed helix, in particular. If you keep rotating in a right-handed way, it will become supercoiled positively, so over-twisted. You over-twist the helix. If you imagine holding one end of the DNA and rotating the bottom of the DNA in a left-hand fashion, then you under-twist the DNA. These two processes drive supercoiling. What that means is that the DNA helix, to compensate for the excess or the under-twist, will coil onto itself. You see this sometimes when you have telephone cords or even little pieces of string. If you start to over-twist them, sometimes they start to coil onto themselves, and this is really also what DNA does inside living cells.
Reading DNA sequences
In bacteria, DNA is intentionally negatively supercoiled. What that means is that bacteria like to keep their DNA underwound. This is because if DNA is underwound — so imagine taking the double-strand helix of DNA and holding one end while you turn counter-clockwise with the other hand — what happens is that the two strands become slightly more open.
© Samanithan Ramakrishnan
They are less packed into this helix; the helix is a little bit more relaxed. It is more open, because it is a right-handed helix. For this reason, what happens is that when you open up this double helix, it is easier for other proteins like RNA polymerase to bind the DNA and read the sequence of DNA. By keeping the DNA negatively supercoiled — so by managing its topology — you can facilitate gene expression.
DNA Knots and links
DNA knots are present in many different organisms. You can form DNA knots in the capsid of viruses. If you ligate the ends of DNA in the virus capsid, you can form knots — very complicated knots. You can also form knots in chromatin. In eukaryotic yeast cells, DNA knots are something of this type; it is a curve that entangles with itself. You cannot really transform this into a simple circle without cutting or gluing something, so by doing continuous deformations, you will never get rid of these crossings here.
© Zephyris via Wikimedia Commons
The third structure is linking. Linking is this type of topological structure present in DNA of parasites, so-called trypanosomes. These are blood-dwelling parasites. They carry nasty diseases in Africa and also in South America, like Chagas disease or sleeping sickness. The mitochondrion of this single-cell parasite contains a structure called kinetoplast DNA that is made of thousands of DNA rings all interlinked together. We do not know why.
We do not know what the evolutionary benefit of having such a topologically complicated structure is, but we call these structures topological structures because you cannot really deform these interlinked rings into separate rings without cutting and gluing. This is what renders DNA topology fascinating. It is present in parasites, bacteria, viruses and higher order organisms. What my group does is try to understand how DNA topology impacts DNA function as well as how we can use DNA topology, perhaps to make new materials.
Managing entangled cells
What is really important and what essentially every living organism, every bacterium, every higher order organism, has is one form of topoisomerase. Topoisomerase is a fantastic protein. The first time I had heard of it, I thought it was magic. It is a protein that can bind DNA and transiently create a cut, open DNA, pass a double strand of DNA through and then glue it back; it can actually do topological operations. It can open the DNA, cut DNA and close it back.
© Davide Michieletto
It can do the operations that otherwise, by doing smooth deformations, would not be able to remove knots and entanglements — but topoisomerase can, by doing this transient break, cutting and gluing. The fact that every living organism has a form of topoisomerase tells you a lot about how important it is to manage entanglement and the DNA topology in the cell. It is really essential for life. When topoisomerases do not work, that is when we get cell death or cancer cells.
Disentangling for division
In cell division, chromosomes are brought together — so sister chromatids are brought together — into the famous X shape. They are brought together at the chromacenter.
© Cred: Ed Uthman, MD
To get to that state (so to that pre-mitotic state before the two chromosomes are divided into the daughter cells) what happens is that the interface, the mass — that packed, dense solution of chromosomes — has to be disentangled. If it was not for the topoisomerase, the chromosomes would also remain entangled during mitosis, during cell division. When the two cells start to divide, they then create a lot of tension, and the DNA breaks. When the DNA breaks, the cell tries to repair them and sometimes repairs them incorrectly, either leading to cell death or to cancer.
DNA topology therapies
DNA topology has an effect not only on the function of DNA itself, but also on how drugs work and how we can come up with medical applications to target DNA topology to treat diseases. We can inhibit what topoisomerase does by coming up with drugs that target topoisomerase.
© Maksym Kozlenko
A group of drugs called quinolones are very strong antibiotics, and these quinolones target DNA gyrase — so this equivalent of topoisomerase that keeps DNA negatively supercoiled. Another very potent anti-cancer drug is called etoposide. This was one of the first anti-cancer drugs ever developed, actually, and targets the type-two topoisomerases, which are the ones that resolve these entanglements. When these drugs bind the protein at certain active sites of the protein, the protein stops working. It cannot resolve the DNA entanglements anymore. These DNA entanglements, when the cell divides, transform into DNA breaks. Then, eventually, the cells die.
Targeted drug discovery
The issue with these drugs is that DNA topoisomerases are everywhere. They are in cancer cells; they are in diseased cells but also in healthy cells. These drugs target all the cells — all the topoisomerases in both diseased and healthy cells — and the problem is that they have a lot of side effects. One of the big challenges in the field of DNA topoisomerase and DNA topology is to try to discover new drugs that selectively target topoisomerases: the topoisomerase in bacteria but not those in humans, or the ones in cancer cells and not those in healthy cells.
There are also technological advances where we can use topoisomerases to cut and glue pieces of DNA into genomes.
© U.S. Department of Energy from United States
This is very similar to what CRISPR does, or recombinant DNA — so using recombination techniques. This is a way to do genome editing that now is a particularly popular topic after the discovery of CRISPR.
DNA topology misconceptions
One misconception about the DNA topology is that it is always bad. The fact that the DNA is knotted, linked, supercoiled or displays this strange topological or often complicated topological structure is not necessarily a bad thing.
Often people ask me, how does DNA knotting negatively affect gene transcription or cell function? It actually could be the other way around; we still do not know. For instance, by knotting and supercoiling DNA, you could package DNA in different ways. DNA being linked with itself offers some kind of evolutionary benefit, such as the fact that during cell division, you do not lose genetic information. DNA topology can also lead to the enhanced functionality of DNA.
Editor’s note: This article has been faithfully transcribed from the original interview filmed with the author, and carefully edited and proofread. Edit date: 2025
Discover more about
DNA topology
Tubiana, L., Alexander, G. P., Barbensi, A., et al. (2024). Topology in soft and biological matter. Physics Reports, 1075, 1–137.
Michieletto, D. (2025).Kinetoplast DNA: A polymer physicist’s topological Olympic dream. Nucleic Acids Research, 53(2), gkae1206.
Orlandini, E., Marenduzzo, D. & Michieletto, D. (2019). Synergy of topoisomerase and structural-maintenance-of-chromosomes proteins creates a universal pathway to simplify genome topology. Proceedings of the National Academy of Sciences of the United States of America, 116(17), 8149–8154.
Michieletto, D., Fosado, Y. A. G., Melas, E., et al. (2022). Dynamic and facilitated binding of topoisomerase accelerates topological relaxation. Nucleic Acids Research, 50(8), 4659–4668.
Michieletto, D., Marenduzzo, D. & Orlandini, E. (2015). Topological patterns in two-dimensional gel electrophoresis of DNA knots. Proceedings of the National Academy of Sciences of the United States of America, 112(40), E5471–E5477.
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