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By P Boisseau; P Houdy; M Lahmani; European Materials Research Society

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9 illustrates schematically the supercoiling phenomenon and the relation between twist and writhe. The difference in supercoiling energy between two topoisomers depends on the square of the change in linking number: ΔGsc = 1 KRT (ΔL)2 N In the above example, (ΔL)2 = 16. It is a striking thing that DNA always has negative supercoiling in bacteria, but positive supercoiling in archaeobacteria, and both geometries in eukaryotes. The degree of supercoiling and its orientation depend on the angle of rotation between consecutive bases, itself determined by the distance between base pairs.

8. Circular DNA helices can arrange themselves in space to form positive or negative supercoils, leading to what are known as topoisomers. The a) b) c) d) Fig. 8. (a) and (b): Relaxed circular DNA. (c) and (d): Supertwisted DNA with negative supercoiling. (a) and (c) are electron microscope images, while (b) and (d) are diagrammatic 1 Structural and Functional Regulation of DNA 1 2 13 3 Fig. 9. Writhe of a straight, doublestranded helix leading to supercoiling. (1) T = 0, W = 0. (2) T = 8, W = 0, L = 8.

A) and (c) are electron microscope images, while (b) and (d) are diagrammatic 1 Structural and Functional Regulation of DNA 1 2 13 3 Fig. 9. Writhe of a straight, doublestranded helix leading to supercoiling. (1) T = 0, W = 0. (2) T = 8, W = 0, L = 8. (3) W = 1, ΔL = 1 supercoiling of DNA is characterised by three parameters: the linking number L, the twist T , and the writhe W . These are related by the simple formula L=T +W . In a relaxed circular DNA, the writhe corresponding to the degree of supercoiling is zero.

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