Chapter 4: Knots and catenanes

To most people the word 'knot' conjures up images of boy scouts and bowlines, but, in the context of this book, it refers to 'topological' knots in DNA. The distinction between the everyday sense of the word 'knot' (as applied, for example, to a shoelace) and a topological knot, is that the latter must be a closed curve. Like linking number (described in Chapter 2), topological knotting is a concept that is only meaningful in a closed curve. Any knot tied in a piece of string becomes a topological knot when the two ends are joined together. 'Catenane' is a less familiar term and refers to the topological interlinking of two or more rings, such as in the links of a chain. In Chapter 2, rubber tubing and ribbon are used to model the behaviour of DNA, and with both these materials we can also make knots and catenanes. It may seem surprising that DNA can form these structures too, but, as this chapter shows, knots and catenanes do indeed occur in DNA and we discuss their occurrence, properties and biological relevance. Since knots and catenanes are topological in nature they can be investigated and understood using similar techniques and concepts to those used for supercoiling. In particular, we describe a classification system (the 'ideal' representation), which can be used to define knots and catenanes fairly straightforwardly.

So, although knots and catenanes can appear to be esoteric structures and their descriptions can involve fairly complex mathematical concepts, they are found in DNA in nature, and their origins may well reflect important features of the reactions of DNA-specific enzymes. Indeed, careful analyses of knots and catenanes generated by such enzymes have yielded important mechanistic information concerning these enzymes (see Chapter 6). Additionally, knots and catenanes have proved to be valuable synthetic tools for probing DNA-protein interactions.

Click on the thumbnails below for full-size versions of the illustrations in Chapter 4.

Alternatively, you can download zip files containing all the figures for Chapter 4 (file 1 and file 2).

Figures

Figure 4.1	Figure 4.2	Figure 4.3
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Figure 4.7