As a helicase moves along unwinding DNA, the DNA in front of the helicase will become overwound in the absence of other changes. As discussed in Section 4.2, DNA double helices that are torsionally stressed tend to fold up on themselves to form tertiary structures created by supercoiling. We will first consider the supercoiling of DNA in quantitative terms and then turn to topoisomerases, enzymes that can directly modulate DNA winding and supercoiling. Supercoiling is most readily understood by considering circular DNA molecules, but it also applies to linear DNA molecules constrained to be in loops by other means. Most DNA molecules inside cells are subject to supercoiling.

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Consider a linear 260-bp DNA duplex in the B-DNA form (Figure 28.15A). Because the number of base pairs per turn in an unstressed DNA molecule averages 10.4, this linear DNA molecule has 25 (260/10.4) turns. The ends of this helix can be joined to produce a relaxed circular DNA (Figure 28.15B). A different circular DNA can be formed by unwinding the linear duplex by two turns before joining its ends (Figure 28.15C). What is the structural consequence of unwinding before ligation? Two limiting conformations are possible. The DNA can fold into a structure containing 23 turns of B helix and an unwound loop (Figure 28.15D). Alternatively, the double helix can fold up to cross itself. Such crossings are called supercoils. In particular, a supercoiled structure with 25 turns of B helix and 2 turns of right-handed (termed negative) superhelix can be formed (Figure 28.15E).

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Supercoiling markedly alters the overall form of DNA. A supercoiled DNA molecule is more compact than a relaxed DNA molecule of the same length. Hence, supercoiled DNA moves faster than relaxed DNA when analyzed by centrifugation or electrophoresis. Unwinding will cause supercoiling in circular DNA molecules, whether covalently closed or constrained in closed configurations by other means.

Our understanding of the conformation of DNA is enriched by concepts drawn from topology, a branch of mathematics dealing with structural properties that are unchanged by deformations such as stretching and bending. A key topological property of a circular DNA molecule is its linking number (Lk), which is equal to the number of times that a strand of DNA winds in the right-handed direction around the helix axis when the axis lies in a plane, as in Figure 28.15A. For the relaxed DNA shown in Figure 28.15B, Lk = 25. For the partly unwound molecule shown in part D and the supercoiled one shown in part E, Lk = 23 because the linear duplex was unwound two complete turns before closure. Molecules differing only in linking number are topological isomers, or topoisomers, of one another. Topoisomers of DNA can be interconverted only by cutting one or both DNA strands and then rejoining them.

The unwound DNA and supercoiled DNA shown in Figure 28.15D and E are topologically identical but geometrically different. They have the same value of Lk but differ in twist (Tw) and writhe (Wr). Although the rigorous definitions of twist and writhe are complex, twist is a measure of the helical winding of the DNA strands around each other, whereas writhe is a measure of the coiling of the axis of the double helix—that is, supercoiling. A right-handed coil is assigned a negative number (negative supercoiling) and a left-handed coil is assigned a positive number (positive supercoiling).

Is there a relation between Tw and Wr? Indeed, there is. Topology tells us that the sum of Tw and Wr is equal to Lk.

In Figure 28.15, the partly unwound circular DNA has Tw ~ 23, meaning the helix has 23 turns and Wr ~ 0, meaning the helix has not crossed itself to create a supercoil. The supercoiled DNA, however has Tw ~ 25 and Wr ~ −2. These forms can be interconverted without cleaving the DNA chain because they have the same value of Lk—namely, 23. The partitioning of Lk (which must be an integer) between Tw and Wr (which need not be integers) is determined by energetics. The free energy is minimized when about 70% of the change in Lk is expressed in Wr and 30% is expressed in Tw. Hence, the most stable form would be one with Tw = 24.4 and Wr = −1.4. Thus, a lowering of Lk causes both right-handed (negative) supercoiling of the DNA axis and unwinding of the duplex. Topoisomers differing by just 1 in Lk, and consequently by 0.7 in Wr, can be readily separated by agarose gel electrophoresis because their hydrodynamic volumes are quite different; supercoiling condenses DNA (Figure 28.16).

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Most naturally occurring DNA molecules are negatively supercoiled. What is the basis for this prevalence? As already stated, negative supercoiling arises from the unwinding or underwinding of the DNA. In essence, negative supercoiling prepares DNA for processes requiring separation of the DNA strands, such as replication. Positive supercoiling condenses DNA as effectively, but it makes strand separation more difficult.

The presence of supercoils in the immediate area of unwinding would, however, make unwinding difficult. Therefore, negative supercoils must be continuously removed, and the DNA relaxed, as the double helix unwinds. Specific enzymes called topoisomerases that introduce or eliminate supercoils were discovered by James Wang and Martin Gellert. Type I topoisomerases catalyze the relaxation of supercoiled DNA, a thermodynamically favorable process. Type II topoisomerases utilize free energy from ATP hydrolysis to add negative supercoils to DNA. Both type I and type II topoisomerases play important roles in DNA replication as well as in transcription and recombination.

These enzymes alter the linking number of DNA by catalyzing a three-step process: (1) the cleavage of one or both strands of DNA, (2) the passage of a segment of DNA through this break, and (3) the resealing of the DNA break. Type I topoisomerases cleave just one strand of DNA, whereas type II enzymes cleave both strands. The two types of enzymes have several common features, including the use of key tyrosine residues to form covalent links to the polynucleotide backbone that is transiently broken.

The three-dimensional structures of several type I topoisomerases have been determined (Figure 28.17). These structures reveal many features of the reaction mechanism. Human type I topoisomerase comprises four domains, which are arranged around a central cavity having a diameter of 20 Å, just the correct size to accommodate a double-stranded DNA molecule. This cavity also includes a tyrosine residue (Tyr 723), which acts as a nucleophile to cleave the DNA backbone in the course of catalysis.

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From analyses of these structures and the results of other studies, the relaxation of negatively supercoiled DNA molecules is known to proceed in the following manner (Figure 28.18). First, the DNA molecule binds inside the cavity of the topoisomerase. The hydroxyl group of tyrosine 723 attacks a phosphoryl group on one strand of the DNA backbone to form a phosphodiester linkage between the enzyme and the DNA, cleaving the DNA and releasing a free 5′-hydroxyl group.

With the backbone of one strand cleaved, the DNA can now rotate around the remaining strand, its movement driven by the release of energy stored because of the supercoiling. The rotation of the DNA unwinds the supercoils. The enzyme controls the rotation so that the unwinding is not rapid. The free hydroxyl group of the DNA attacks the phosphotyrosine residue to reseal the backbone and release tyrosine. The DNA is then free to dissociate from the enzyme. Thus, reversible cleavage of one strand of supercoiled DNA allows controlled rotation to partly relax the supercoils.

Supercoiling requires an input of energy because a supercoiled molecule, in contrast with its relaxed counterpart, is torsionally stressed. The introduction of an additional supercoil into a 3000-bp plasmid typically requires about 30 kJ mol⁻¹ (7 kcal mol⁻¹).

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Supercoiling can be catalyzed by type II topoisomerases. These elegant molecular machines couple the binding and hydrolysis of ATP to the directed passage of one DNA double helix through another, temporarily cleaved DNA double helix. These enzymes have several mechanistic features in common with the type I topoisomerases.

Topoisomerase II molecules are dimeric with a large internal cavity (Figure 28.19). The large cavity has gates at both the top and the bottom that are crucial to topoisomerase action. The reaction begins with the binding of one double helix (hereafter referred to as the G, for gate, segment) to the enzyme (Figure 28.20). Each strand is positioned next to a tyrosine residue, one from each monomer, capable of forming a covalent linkage with the DNA backbone. This complex then loosely binds a second DNA double helix (hereafter referred to as the T, for transported, segment). Each monomer of the enzyme has a domain that binds ATP; this ATP binding leads to a conformational change that strongly favors the coming together of the two domains. As these domains come closer together, they trap the bound T segment. This conformational change also forces the separation and cleavage of the two strands of the G segment. Each strand is linked to the enzyme by a tyrosine–phosphodiester bond. Unlike the type I enzymes, the type II topoisomerases hold the DNA tightly so that it cannot rotate. The T segment then passes through the cleaved G segment and into the large central cavity. The ligation of the G segment leads to the release of the T segment through the gate at the bottom of the enzyme. The hydrolysis of ATP and the release of ADP and orthophosphate allow the ATP-binding domains to separate, preparing the enzyme to bind another T segment. The overall process leads to a decrease in the linking number by two.

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The bacterial topoisomerase II (often called DNA gyrase) is the target of several antibiotics that inhibit the prokaryotic enzyme much more than the eukaryotic one. Novobiocin blocks the binding of ATP to gyrase. Nalidixic acid and ciprofloxacin, in contrast, interfere with the breakage and rejoining of DNA chains. These two gyrase inhibitors are widely used to treat urinary tract and other infections including those due to Bacillus anthracis (anthrax). Camptothecin, an antitumor agent, inhibits human topoisomerase I by stabilizing the form of the enzyme covalently linked to DNA.