From boat ropes to shoelaces, knots are found everywhere in our day-to-day lives. But where things really get tied up is on the microscopic scale. Even the basic code for life inside our cells can sometimes be prone to tangles. So, why exactly are knots found in our DNA, and what are the biological causes?
During her math colloquium on November 21, Professor Candice Price from Smith College presented her research findings. Price conducts research in DNA topology, applying knot theory onto DNA structure.
The branch of mathematics discussed here—knot theory—studies the properties of mathematical knots. While our shoelaces and boating knots can be untied, this theoretical category of knots has joint ends. This means that they cannot be “untied” in the same way as our physical examples; these knots are continuous and non-intersecting!
Though mathematical knots cannot be physically untied, they can be simplified. By using Reidemeister moves, one can change a knot’s diagram (or in a way, physical appearance) without fundamentally modifying its structure. This allows us to prove that a complicated-looking knot is equivalent to a more simplified form. There are three Reidemeister moves, each manipulating a knot differently.
By deforming one knot into another using a series of Reidemeister moves, you can prove their equivalence.
Alternatively, to show that two knots are distinct, one can look toward knot invariants, which are properties of knot classes (i.e., anything related to structure/function) that remain unchanged even after experiencing deformation.
Studying knot theory can help us better understand the physical world. In Professor Price’s case, she harnessed this concept to uncover explanations for knotting in our DNA.
Professor Price addressed three types of proteins that create knots in our DNA: Type I and Type II topoisomerases, and site-specific recombinase.
The type I topoisomerase is a protein that cuts one strand in the DNA double helix, widening its twist before resealing the strand (see figure above). Pulling apart the strands exposes the DNA, creating more space for on-site agents to replicate and transcribe it. Separating the strands can also cause tension on the ends of the DNA. Both topoisomerases relieve the coiling.
The type II topoisomerase protein cuts both strands of a DNA’s double helix, passes another unbroken strand of DNA through it, and then re-seals the originally severed strand. By relaxing and rejoining DNA, the type II topoisomerase eases the process of transcription and prevents the strands from twisting (supercoiling).
In both instances, topoisomerase is responsible for unknotting DNA. Though scientists can use this protein to create knots, it also comes in handy for replication, transcription, and unknotting. Overall, topoisomerases are a crucial tool for undoing DNA knots and relieving tension.
Our genetic material ideally should not become tangled. Otherwise, the cell could face errors in DNA replication, transcription, and gene expression.
Unlike the previous two proteins, the third—site-specific recombinase—fundamentally manipulates our DNA by modifying its topology. It performs this to create genetic diversity ahead of cell division. In short, this protein is capable of “cutting and pasting” genetic material (i.e., taking out information and binding it elsewhere). While “cutting and pasting,” the site-specific recombinase can create some knotting. This is because the breaking and rejoining may result in twisting of strands.
All of this knotting makes scientists curious about its underpinnings, and that is precisely where Price’s research on knot theory comes in. Reidemeister moves can be used to examine the structure of knotted DNA and determine the cause of entanglement. With this, researchers can also explore how knots can be untangled with other proteins (e.g., site-specific recombinase).
Ultimately, the contributions of researchers including Price greatly clarify DNA topology, making its knotting phenomenon much less daunting. So, while living organisms are no doubt complicated, studying their genetic material doesn’t necessarily have to be.
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