# Knotty Developments with DNA

Karin Valencia is a PhD student in Imperial’s DNA Topology research group.

The term ‘DNA structure’ may bring to mind any number of things, from the television drama CSI to the famous double helix. Perhaps less familiar are the ‘higher-order’ structural features of DNA, namely knots. DNA in nature can be found to be ‘knotted’ or ‘linked’, reflecting important features of certain proteins inside our cells – those specialised machines that work hard to keep our bodies functioning.

Knots are eccentric structures, and their connection to DNA isn’t immediately obvious. However, it is now known that knotting is unavoidable when dealing with virtually any naturally-occurring DNA molecule. Because of this, they can reflect important DNA reactions inside our cells, and so have proved to be valuable tools for investigating DNA–protein interactions. Careful analysis of these proteins has also allowed scientists to use their mechanistic features in developing biotechnological tools, pharmaceuticals and genetic engineering. A collaboration between the ‘mathematical theory of knots’ and molecular biology is born!

Knot theory is a field in mathematics. Any knot tied in a piece of string becomes a mathematical knot when the two ends are joined together to make the string ‘closed’ (not the case with our shoelaces). The easiest way to generate this is to take a length of string and pass one end around the other, forming a simple overhand knot, and then fuse the ends together.

In 1877 Peter G. Tait, a Scottish physicist, became inspired by the idea that the chemical properties of elements were related to the knotting that occurs between atoms. He sought a list that included all different types of knots. When Tait began his work, the formal mathematics needed to address the study was unavailable. Ever since, theorists have been inspired to develop a way of proving that knots are distinct. Work at the turn of the century placed the subject on firm mathematical ground. Tait’s work is not nearly finished, and generating such a list remains one of the most significant problems in knot theory – there are 1,701,936 distinct knots with at most 16 crossings! However, knot theory has been the driving force behind some of the most important studies of protein reactions involving DNA.

Of all biological molecules, DNA has perhaps most fired the imagination of scientists and non-scientists alike. Naturally-occurring DNA knots were only first observed in the 1960s by molecular biologist James Wang.  The origin of knots in DNA is likely to be the result of various cellular processes in conjunction with a very long piece of DNA, all confined within the small nucleus. If a human cell nucleus, which always contains 46 chromosomes, is enlarged to the size of a basketball, the total length of the DNA would stretch to 150 miles. Human DNA, therefore, may have vast amounts of knots.

As a by-product of their main purpose, certain proteins working on DNA leave a footprint on the molecule in the form of knots – for example, changing one knot into another.  Knot theorists help understand the mechanisms of these proteins by providing a precise definition of what a knot is, listing all possible results from various reactions, and explaining exactly how one DNA knot can be transformed into another.

In this way, knot theory has been instrumental in the understanding of certain very useful proteins called ‘site-specific recombinases’. They are naturally responsible for altering the genetic code of an organism by, for example, integrating a block of alien DNA into the molecule. They give scientists precise and efficient ways of manipulating DNA and have recently been used in the development of new gene-therapy tools.

Genes are the basic functional units of heredity. They are specific sequences in DNA that encode instructions on how to make proteins. Genetic disorders can result when faulty genes encode proteins that are unable to carry out their normal functions, and gene therapy is a technique for correcting these faults. The idea is to devise a means of transport, to put ‘healthy’ artificial genes into our cells and thus restore cells to their normal healthy state.  Site-specific recombinases are used to insert healthy genes into very short pieces of circular DNA, which are proving to be promising tools for the transport of healthy genes.

Biology and mathematics have hardly been the closest of friends, but this is rapidly changing. Knot theory has been the driving force behind the systematic understanding of DNA-protein interactions, something that has led to the development of a new and exciting therapies for inherited diseases.

Image from bentobjects.blogspot.com