But imagine trying to replicate that process on the molecular level.

Why knot: knots, molecules and stick numbers

In other words, none of these three can be rearranged to look like the others. Fig 13: In fact, every p,q -torus knot is also a q,p -torus knot. Fig 3: Hidden within these simple objects is an amazing amount of mathematics, with essential implications for physics, chemistry, biology and the other sciences.

We call the least number of sticks for a knot K the stick number of K, denoted s K. Translated back to chemistry, this is relevant to the question of how long a molecular chain is necessary to construct a knotted molecule in the shape of a particular knot.

This site uses cookies from Google and other third parties to deliver its services, to personalise adverts and to analyse traffic. He is particularly interested in the mathematical theory of knots and their applications.

The vertices labelled with P are to be thought of as lying in the plane of the screen. So far, the simplest knotted molecule constructed appears in Figure 9, its first synthesis dating from the year 2000.

A mathematical knot. A cyclic molecule and a knotted molecule with the same constituent atoms. Research Light pulse peels crystal layers off parent 25 February 2019 Partial cisâ€”trans isomerisation in photoactive organic molecule results in controlled fragmentation. What about four sticks? Well, let's suppose that we could make a nontrivial knot out of five sticks glued end-to-end.

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It turns out that there are enzymes in the nucleus that will perform knot theoretic operations on the DNA molecule that allow it to knot and unknot. The second part of the argument is to show that the knots cannot be constructed with fewer sticks.

It might be that one of the sticks bends in the plane perpendicular to the picture, but we can't see that.

The p,q - torus knot. Here is a picture of a trefoil knot constructed with six sticks:. Registration is free, quick and easy. You can see an animated version of this picture by downloading Flash Player 5 and ensuring that Javascript is enabled, and then reloading this page. Fig 10: So far, over 1. At the beginning of civilization, knots would have been used to tie on rudimentary clothing, to secure weapons to the body, to create shelters.