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Chapter 24 Genes and Chromosomes

Figure Linking Number

Nick

FIGURE 24-16 Linking number applied to closed-circular DNA molecules. A 2,100 bp circular DNA is shown in three forms: (a) relaxed, Lk = 200; (b) relaxed with a nick (break) in one strand, Lk undefined; and (c) underwound by two turns, Lk = 198. The underwound molecule generally exists as a supercoiled molecule, but underwinding also facilitates the separation of DNA strands.

Nick

FIGURE 24-16 Linking number applied to closed-circular DNA molecules. A 2,100 bp circular DNA is shown in three forms: (a) relaxed, Lk = 200; (b) relaxed with a nick (break) in one strand, Lk undefined; and (c) underwound by two turns, Lk = 198. The underwound molecule generally exists as a supercoiled molecule, but underwinding also facilitates the separation of DNA strands.

in the DNA (in its B form) have been removed. The degree of underwinding in cellular DNAs generally falls in the range of 5% to 7%; that is, a = -0.05 to -0.07. The negative sign indicates that the change in linking number is due to underwinding of the DNA. The supercoil-ing induced by underwinding is therefore defined as negative supercoiling. Conversely, under some conditions DNA can be overwound, resulting in positive su-percoiling. Note that the twisting path taken by the axis of the DNA helix when the DNA is underwound (negative supercoiling) is the mirror image of that taken when the DNA is overwound (positive supercoiling) (Fig. 24-17). Supercoiling is not a random process; the path of the supercoiling is largely prescribed by the torsional strain imparted to the DNA by decreasing or increasing the linking number relative to B-DNA.

Linking number can be changed by ±1 by breaking one DNA strand, rotating one of the ends 360° about the unbroken strand, and rejoining the broken ends. This change has no effect on the number of base pairs or the number of atoms in the circular DNA molecule. Two forms of a circular DNA that differ only in a topological property such as linking number are referred to as topoisomers.

Linking number can be broken down into two structural components called writhe (Wr) and twist (Tw) (Fig. 24-18). These are more difficult to describe than linking number, but writhe may be thought of as a measure of the coiling of the helix axis and twist as deter-

Relaxed DNA Lk = 200

Negative supercoils Lk = 198

Positive supercoils Lk = 202

FIGURE 24-17 Negative and positive supercoils. For the relaxed DNA molecule of Figure 24-1 6a, underwinding or overwinding by two helical turns (Lk = 198 or 202) will produce negative or positive supercoiling, respectively. Note that the DNA axis twists in opposite directions in the two cases.

mining the local twisting or spatial relationship of neighboring base pairs. When the linking number changes, some of the resulting strain is usually compensated for by writhe (supercoiling) and some by changes in twist, giving rise to the equation

Tw and Wr need not be integers. Twist and writhe are geometric rather than topological properties, because they may be changed by deformation of a closed-circular DNA molecule.

In addition to causing supercoiling and making strand separation somewhat easier, the underwinding of

Straight ribbon (relaxed DNA)

Straight ribbon (relaxed DNA)

Large writhe, small change in twist

Large writhe, small change in twist

Zero writhe, large change in twist

FIGURE 24-18 Ribbon model for illustrating twist and writhe. The pink ribbon represents the axis of a relaxed DNA molecule. Strain introduced by twisting the ribbon (underwinding the DNA) can be manifested as writhe or twist. Changes in linking number are usually accompanied by changes in both writhe and twist.

DNA facilitates a number of structural changes in the molecule. These are of less physiological importance but help illustrate the effects of underwinding. Recall that a cruciform (see Fig. 8-21) generally contains a few unpaired bases; DNA underwinding helps to maintain the required strand separation (Fig. 24-19). Underwinding of a right-handed DNA helix also facilitates the formation of short stretches of left-handed Z-DNA in regions where the base sequence is consistent with the Z form (Chapter 8).

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