Topoisomerases and Linking Number

Linking number (Lk) counts the number of times one strand of a closed DNA molecule winds around the other; it is a topological invariant, fixed the moment the last phosphodiester bond seals a circle. Lk partitions into twist (Tw, the local helical winding) and writhe (Wr, the coiling of the helix axis in three-dimensional space), related by Lk = Tw + Wr. Supercoiling is simply the departure of Lk from its relaxed value, Lk₀ = N/10.5, where N is the number of base pairs. Because Lk is a topological property, it cannot be changed by bending, stretching, or any deformation that does not break a phosphodiester backbone — a mathematical fact, not a biochemical one, and it is exactly this rigidity that makes topoisomerases necessary. Topoisomerases are the only enzymes that can alter Lk, and they do so by a controlled, transient breakage of the DNA backbone. Type I topoisomerases nick one strand of the duplex, allow the intact strand to pass through the transient single-strand gap (or, in some sub-families, allow controlled rotation of the cut strand around the intact one), then reseal the nick. Because only one strand is broken, each catalytic event changes Lk by exactly ±1. Type II topoisomerases instead make a transient double-strand break in one DNA duplex (the "gate" segment, G-segment), physically pass a second, intact duplex segment (the "transported" segment, T-segment) through the gap, and reseal the break. Because an entire duplex passes through another, each catalytic cycle changes Lk by exactly ±2, and because this large-scale double-strand gating and re-ligation is energetically demanding, all known type II enzymes require ATP hydrolysis. A further distinction concerns mechanism of strand rotation versus strand passage, and the covalent chemistry of religation. Type I enzymes form a transient covalent phosphotyrosine bond to the cut DNA (linking either the 5′ or the 3′ end of the break to the enzyme, depending on subfamily — IA versus IB), which conserves the phosphodiester bond energy and allows resealing without an external energy source. Type II enzymes also use a covalent phosphotyrosine intermediate (on the 5′ ends of both cut strands, working as a homodimer or heterotetramer), but they additionally use ATP binding and hydrolysis to drive the large conformational changes needed to clamp, cut, transport, and release DNA through two duplex-sized "gates." These enzyme classes together explain essentially every observed change in DNA linking number in a living cell.

Type IA topoisomerases (e.g., bacterial topoisomerase I/topA, topoisomerase III) act on single-stranded or locally underwound/negatively supercoiled DNA. The enzyme binds a single strand at a transiently opened region, cleaves it, forming a 5′-phosphotyrosine covalent enzyme-DNA intermediate, and opens like a hinged clamp. The intact complementary strand (or another single strand, in decatenation reactions) is passed through the resulting gap in a strand-passage mechanism, and the break is resealed. Because the substrate is a single strand, type IA enzymes relax only negative supercoils (underwinding) in most organisms, changing Lk by +1 per catalytic cycle, and they require no ATP because the covalent enzyme-DNA bond conserves the energy of the broken phosphodiester bond.

Type IB topoisomerases (e.g., eukaryotic topoisomerase I, vaccinia topoisomerase) work differently: the enzyme nicks one strand, forming a 3′-phosphotyrosine linkage, but instead of strand passage through a gap, it allows the downstream duplex to rotate freely (a "controlled rotation" or "swivelase" mechanism) around the intact strand, dissipating both positive and negative supercoiling before religation. Because rotation can proceed through multiple turns before resealing, a single binding event can change Lk by more than one unit, though the minimal unit of chemistry is still one cut strand per event.

Type II topoisomerases (bacterial DNA gyrase and topoisomerase IV; eukaryotic topoisomerase IIα/β) operate as dimers with a characteristic three-gate ("two-gate" DNA plus ATPase gate) clamp architecture. The steps of a canonical type II reaction cycle: 1. The enzyme binds a G-segment (gate segment) of duplex DNA and captures a second T-segment (transported segment), often the same duplex elsewhere along its length (for supercoil relaxation) or a different duplex (for decatenation of replicated circles). 2. ATP binding to the N-terminal ATPase domains drives dimerization of the ATPase "clamp," trapping the T-segment. 3. The enzyme cleaves both strands of the G-segment, each cut forming a covalent 5′-phosphotyrosine bond to one subunit, opening a transient double-strand gate. 4. The T-segment is passed through this open gate into the space below. 5. The G-segment is religated, restoring an intact duplex on the far side, and the T-segment exits through a C-terminal "exit gate." 6. ATP hydrolysis and Pi/ADP release reset the enzyme for another cycle. Each full cycle changes Lk by exactly 2 and consumes two ATP. Crucially, DNA gyrase, found chiefly in bacteria, uses this same machinery but wraps DNA around itself in a defined chiral (positive) sense before strand passage, so that its net catalytic activity actively introduces negative supercoils (decreasing Lk) using ATP hydrolysis, rather than merely relaxing existing supercoiling. Eukaryotic topoisomerase II and bacterial topoisomerase IV, in contrast, relax supercoils of either sign and are the principal enzymes that unlink (decatenate) daughter DNA circles/chromosomes after replication.

Where supercoiling comes from, and how topoisomerases respond. Two enzymes that translocate along DNA while tracking one groove — replicative helicases and RNA polymerase — generate a wave of positive supercoiling ahead of them (over-winding, because the strands must unwind locally but the far ends are constrained) and, for replication, entangled precatenanes or negative supercoiling in the newly replicated region behind. This is the twin-supercoiled-domain model (Liu and Wang, 1987). In bacteria, gyrase relaxes the positive supercoils ahead of the fork/polymerase (net negative supercoiling injected, ATP-dependent), while topoisomerase I relaxes excess negative supercoiling that can accumulate behind transcribing polymerases. In eukaryotes, topoisomerase I and topoisomerase II both relax positive supercoiling ahead of forks and polymerases (topoisomerase I by controlled rotation, requiring no ATP; topoisomerase II by strand passage, requiring ATP), and topoisomerase II is essential afterward for decatenating the two daughter DNA duplexes so that sister chromatids can be segregated at mitosis.

James Wang and the discovery of the ω protein (1971). Working with E. coli extracts, James C. Wang identified an activity that could convert negatively supercoiled, covalently closed circular DNA into a form with reduced superhelical density, changing its sedimentation and electrophoretic mobility, without changing the covalent continuity of the circle. Crucially, agarose gel electrophoresis of the products showed a ladder of discrete topoisomers, each differing from its neighbor by exactly one unit of linking number — direct physical proof that the enzyme (which Wang called the "ω protein," later renamed E. coli topoisomerase I) removes supercoils one Lk unit at a time. This was the founding observation of the entire topoisomerase field and the first demonstration that a specific protein activity, not merely thermal fluctuation, controls DNA topology.

Proof that changes occur one at a time (type I) versus two at a time (type II). The definitive evidence came from two-dimensional and one-dimensional gel electrophoresis of topoisomer distributions. When a population of covalently closed circular plasmids with a distribution of linking numbers is treated briefly with purified E. coli topoisomerase I, gel electrophoresis resolves a ladder of bands each separated by ΔLk = 1. When the same substrate is treated with a type II enzyme such as DNA gyrase or eukaryotic topoisomerase II, the ladder instead shows bands separated by ΔLk = 2, with the odd-numbered intermediate topoisomers absent — a clean and unambiguous biochemical signature distinguishing the two mechanisms, confirmed across many labs through the 1970s–1980s.

Gellert, Mizuuchi, O'Dea, and Nash (1976): discovery of DNA gyrase. This group identified a bacterial enzyme activity that, remarkably, could introduce negative supercoils into a relaxed closed circular DNA molecule — the opposite of a simple relaxing activity — and showed this required ATP hydrolysis. This was direct proof that some topoisomerases are not passive relaxases but active, energy-consuming machines capable of driving DNA away from its topological equilibrium. Subsequent work showed gyrase is a heterotetramer (GyrA₂GyrB₂) and is the molecular target of two major antibiotic classes, quinolones (bind the GyrA-DNA cleavage complex) and aminocoumarins such as novobiocin (block the GyrB ATPase site) — pharmacological evidence that independently confirmed the two functional domains predicted by the biochemical mechanism.

Strand-passage proof for type II enzymes using knotted and catenated DNA. A separate line of decisive evidence came from using topologically linked (catenated) or knotted DNA circles as substrates. Only an enzyme capable of passing one intact duplex through a transient break in another can unknot a knotted circle or unlink (decatenate) two interlocked circles without breaking the sugar-phosphate backbone permanently. Purified type II topoisomerases (gyrase, topoisomerase IV, eukaryotic topoisomerase II) were shown to efficiently unknot and decatenate such substrates in vitro in an ATP-dependent manner, while type I enzymes could not, providing clean genetic and biochemical separation of the two mechanisms and explaining, later, why topoisomerase II (not topoisomerase I) is essential for separating replicated sister chromatids in vivo — a fact confirmed by temperature-sensitive topoisomerase II mutants in yeast that arrest with unresolved, catenated sister chromosomes at the non-permissive temperature (Holm et al., 1985; DiNardo et al., 1984).

Example 1 — quantifying Lk change during plasmid relaxation. A covalently closed circular plasmid has N = 4,200 bp and a relaxed linking number Lk₀ = N/10.5 ≈ 400. In vivo it is maintained at a superhelical density σ = (Lk − Lk₀)/Lk₀ = −0.06, typical of bacterial chromosomal DNA. Step 1: Solve for actual Lk. Lk − Lk₀ = σ × Lk₀ = (−0.06)(400) = −24. So Lk = 400 − 24 = 376 (24 fewer links than relaxed — negatively supercoiled). Step 2: How many catalytic cycles does each enzyme type need to fully relax this plasmid (bring Lk to 400)?

• Type IA topoisomerase (ΔLk = +1 per event, relaxes negative supercoils only): needs 24 separate catalytic cycles.
• Type II topoisomerase (ΔLk = +2 per event, ATP-dependent): needs 12 catalytic cycles, consuming 24 ATP (2 ATP per cycle).

This illustrates directly why gel ladders from type I versus type II digestion look different (steps of 1 versus steps of 2) and why full relaxation by a type II enzyme costs a defined, countable amount of ATP — 2 per unit of Lk changed.

Example 2 — a replication topology problem. A circular bacterial chromosome-mimic plasmid of 46,000 bp is replicated bidirectionally from a single origin. Assume, for simplicity, that as the two forks proceed, the region already replicated becomes two interlinked (catenated) daughter circles, and ignore supercoiling ahead of the forks for this calculation (that part is handled separately by gyrase, as above). If replication proceeds to completion, the two daughter duplexes remain topologically linked with a catenation number equal to (in the simplest case) the original number of helical turns in the unreplicated template, ~46,000/10.5 ≈ 4,381 links, though in practice replication and recombination reduce this to a much smaller residual catenation number by the time forks converge, typically in the range of tens of interlinks per chromosome equivalent in bacteria. Suppose after replication the two sister circles are linked with a residual catenation number of 20 (a plausible order-of-magnitude figure for a plasmid-sized replicon in vivo). Only topoisomerase IV (a type II enzyme in bacteria; topoisomerase II in eukaryotes) can resolve this, because unlinking two separate closed circles requires passing one entire duplex through a transient double-strand break in the other — impossible for any type I enzyme. Number of catalytic (strand-passage) cycles required = catenation number / 2 (since each type II cycle changes the linking number between the two circles by 2) = 20/2 = 10 cycles, consuming 20 ATP. If topoisomerase IV is inhibited (e.g., pharmacologically), the daughter chromosomes cannot separate; in bacterial cell biology this produces the classic phenotype of anucleate cells and chained, unsegregated nucleoids — a phenotype directly observed in topoisomerase IV conditional mutants and quinolone-treated cells.

James C. Wang trained as a physical chemist before turning to the biochemistry of DNA structure, and his defining insight was recognizing that a change in DNA sedimentation behavior in bacterial extracts reflected a change in a discrete topological quantity, not a vague conformational shift. His 1971 paper describing the E. coli ω protein (topoisomerase I) opened an entire field: within a decade, Martin Gellert's group had discovered DNA gyrase, and eukaryotic topoisomerases I and II had been purified and characterized, with structural biology later revealing the extraordinary clamp-and-gate architecture that lets a single enzyme thread an entire DNA duplex through a transient break in another. Wang continued to work on topoisomerase mechanism and genome topology throughout his career at Berkeley and Harvard, linking the biochemistry of strand passage to its physiological roles in replication, transcription, and chromosome segregation.

Topoisomerases sit at the center of major classes of clinically important drugs. Fluoroquinolone antibiotics (ciprofloxacin, levofloxacin) selectively trap the bacterial gyrase and topoisomerase IV cleavage complexes, converting normal transient breaks into lethal, persistent double-strand breaks — exploiting the mechanistic detail that bacterial type II enzymes differ enough in structure from human topoisomerase II to allow selective targeting. Anticancer topoisomerase poisons, such as etoposide (targets human topoisomerase II) and camptothecin/irinotecan (targets human topoisomerase I), work by the same logic in reverse: they stabilize the covalent cleavage complex in rapidly dividing tumor cells, triggering replication-associated double-strand breaks and apoptosis. In biotechnology, type IB topoisomerase (from vaccinia virus) is exploited directly in "TOPO cloning" kits, where the enzyme's covalent 3′-phosphotyrosine intermediate is used to ligate PCR products into vectors without conventional ligase chemistry. Understanding gyrase's unique ATP-dependent negative-supercoiling activity also underlies ongoing antibiotic development, since gyrase has no close functional counterpart in humans, making it an attractively selective drug target as resistance to older quinolones spreads.

Ask the tutor: How does the covalent phosphotyrosine intermediate differ mechanistically between type IA, IB, and type II topoisomerases, and why does this determine their ATP dependence?