2.4 DNA Topology
The mathematics of DNA coiling, superhelicity, and the enzymes that control it
Introduction to DNA Topology
DNA topology refers to the three-dimensional configuration of the DNA double helix, particularly how the two strands are intertwined and how the helical axis coils in space. Unlike simple geometric properties, topological properties cannot be changed without breaking covalent bonds in the DNA backbone.
In cells, DNA is not a relaxed molecule floating freely—it is constrained, twisted, and organized. Understanding DNA topology is crucial because:
- Replication: The replisome must unwind DNA ahead of the fork, creating topological stress
- Transcription: RNA polymerase generates positive supercoils ahead and negative behind
- Recombination: DNA strand exchange creates complex topological intermediates
- Packaging: Chromosomal DNA must be compacted 10,000-fold while remaining accessible
Fundamental Topological Concepts
Closed vs. Open DNA
Topologically Closed
- • Circular DNA (plasmids, bacterial chromosomes)
- • Linear DNA with fixed ends (eukaryotic loops)
- • DNA bound to protein complexes
- • Linking number is invariant
Topologically Open
- • Linear DNA with free ends
- • Can rotate freely to relieve stress
- • No defined linking number
- • Found in vitro, rarely in cells
Topological Domains
Even linear chromosomes are organized into topologically isolated domains where supercoiling is confined:
Bacterial
~50-100 domains per chromosome, ~10 kb each, bounded by DNA-binding proteins
Eukaryotic
Chromatin loops 30-300 kb, anchored by CTCF and cohesin at TAD boundaries
Function
Isolate transcriptional effects, prevent supercoil propagation, organize genome
The Linking Number Equation
The fundamental equation of DNA topology
The linking number (Lk) equals the sum of twist (Tw) and writhe (Wr). For topologically closed DNA, Lk is an integer invariant.
Lk (Linking Number)
- Definition: Number of times one strand crosses the other when DNA is laid flat
- Property: Topological invariant—cannot change without cutting DNA
- Integer: Always a whole number for closed circles
- Sign: Positive for right-handed helix
Tw (Twist)
- Definition: Number of helical turns of one strand around the other
- B-DNA: 1 turn per 10.5 bp (Tw = N/10.5)
- Variable: Can be non-integer, depends on local structure
- Measured: Along the helical axis
Wr (Writhe)
- Definition: Coiling of the helical axis in 3D space
- Supercoiling: Visible as plectonemic or toroidal coils
- Variable: Can be non-integer, geometry-dependent
- Interconvertible: With Tw at constant Lk
Relaxed vs. Supercoiled DNA
For relaxed circular DNA:
Where N = number of base pairs, h = helical repeat
Supercoiling is measured by:
σ = superhelical density (typically -0.05 to -0.07 in vivo)
DNA Supercoiling
Negative Supercoiling (−)
- ΔLk < 0: Underwound DNA
- Effect: Favors strand separation
- Helix: Right-handed supercoils (same as DNA)
- In vivo: Most cellular DNA is negatively supercoiled
- Function: Facilitates replication, transcription initiation
Biological significance: Stores free energy that can be used to drive strand separation during DNA transactions
Positive Supercoiling (+)
- ΔLk > 0: Overwound DNA
- Effect: Opposes strand separation
- Helix: Left-handed supercoils
- Generated: Ahead of replication forks and transcribing polymerases
- Hyperthermophiles: Use (+) supercoiling for genome stability
Danger: Must be removed or DNA transactions stall; topoisomerase inhibition causes replication fork arrest
Supercoil Geometries
Plectonemic (Interwound)
- • DNA axis wraps around itself
- • Branch points and loops
- • Predominant in free DNA
- • Visualized by EM as "figure-8" shapes
Toroidal (Solenoidal)
- • DNA wound around a central axis
- • Like thread on a spool
- • Nucleosome wrapping is toroidal
- • More compact packaging
The Twin-Domain Model of Transcription
As RNA polymerase transcribes DNA, it cannot rotate around the helix axis. Instead:
Ahead (+)
Positive supercoils accumulate ahead of RNAP
Behind (−)
Negative supercoils form behind RNAP
Solution
Topoisomerases resolve both domains
Topoisomerases: The Topology Managers
Topoisomerases are essential enzymes that modulate DNA topology by transiently breaking and rejoining DNA strands. They are absolutely required for DNA replication, transcription, and chromosome segregation.
Type I Topoisomerases
Mechanism
- • Cut ONE DNA strand
- • Form covalent enzyme-DNA intermediate
- • Pass intact strand through break OR rotate
- • Reseal the break
- • Change Lk by ±1 per cycle
Subtypes
Energy
No ATP required. Uses torsional stress energy in DNA. Can only relax (remove) supercoils, not introduce them.
Type II Topoisomerases
Mechanism
- • Cut BOTH DNA strands (DSB)
- • Create a "gate" in one duplex
- • Pass another duplex through
- • Reseal the gate
- • Change Lk by ±2 per cycle
Key Enzymes
Energy
Requires ATP hydrolysis. Can work against torsional stress. Gyrase can introduce (−) supercoils de novo.
Topoisomerase Comparison Table
| Enzyme | Type | ΔLk | ATP | Function | Inhibitors |
|---|---|---|---|---|---|
| E. coli Topo I | IA | +1 | No | Relax (−) supercoils | — |
| E. coli Topo III | IA | ±1 | No | Decatenation, recombination | — |
| Euk. Topo I | IB | ±1 | No | Relax (+) and (−) | Camptothecin, Irinotecan |
| DNA Gyrase | IIA | −2 | Yes | Introduce (−) supercoils | Quinolones, Novobiocin |
| Topo IV | IIA | ±2 | Yes | Decatenation | Quinolones |
| Euk. Topo IIα/β | IIA | ±2 | Yes | Decatenation, relaxation | Etoposide, Doxorubicin |
The Phosphotyrosine Intermediate
All topoisomerases form a covalent intermediate where an active-site tyrosine attacks the DNA phosphodiester backbone:
Type IA & IIA
5′-phosphotyrosine linkage
Free 3′-OH for strand passage
Type IB
3′-phosphotyrosine linkage
Free 5′-OH for religation
Clinical Significance: Topoisomerase poisons (camptothecin, etoposide, quinolones) stabilize this covalent intermediate, converting the enzyme into a DNA-damaging agent. Collision with replication forks converts the transient break into a lethal double-strand break.
DNA Gyrase: A Unique Enzyme
DNA gyrase is the only topoisomerase that can introduce negative supercoils into DNA, making it essential for bacterial survival and a major antibiotic target.
Structure
- Composition: A₂B₂ heterotetramer
- GyrA: Contains active-site tyrosine for cleavage
- GyrB: Contains ATPase domain
- C-terminal domain (CTD): Wraps DNA around enzyme
Mechanism
- CTD wraps ~130 bp of DNA around enzyme
- This wrapping introduces (+) crossover
- GyrA cleaves G-segment (Gate)
- T-segment (Transport) passes through
- Gate reseals: net change Lk = −2
- ATP hydrolysis resets enzyme
Antibiotic Targets
Quinolones (e.g., Ciprofloxacin)
- • Target: GyrA subunit
- • Mechanism: Stabilize cleavage complex
- • Effect: Convert gyrase into DNA poison
- • Resistance: GyrA mutations (Ser83, Asp87)
Aminocoumarins (e.g., Novobiocin)
- • Target: GyrB subunit
- • Mechanism: Compete with ATP binding
- • Effect: Inhibit ATPase, prevent turnover
- • Less used clinically but important tool
Catenanes, Knots, and Complex Topology
Catenanes
Interlocked circular DNA molecules that arise during replication of circular genomes.
- Formation: Convergence of replication forks on circular DNA
- Problem: Daughter circles remain linked
- Solution: Type II topoisomerases (Topo IV, Topo II)
- Catastrophe: Failure → chromosome non-disjunction
DNA Knots
Self-intertwined DNA molecules that can form during recombination and replication.
- Origin: Recombination intermediates, replication errors
- Complexity: Described by knot theory (trefoil, figure-8)
- Resolution: Type II topoisomerases unknot DNA
- Model organism: Studied in bacteriophage P4
Topological Problems in DNA Replication
1. Supercoil Accumulation
As the replisome advances, it cannot rotate around DNA. Positive supercoils accumulate ahead at ~100 per second. Without topoisomerases, fork stalls after 1 second.
2. Pre-catenanes
If supercoils behind the fork are not removed, they distribute around daughter duplexes as pre-catenanes (intertwining of daughter DNAs before replication completes).
3. Terminus Resolution
At the terminus, converging forks cannot simply melt apart—remaining links must be resolved by Topo IV. This is rate-limiting for chromosome segregation.
Biological Importance of DNA Topology
Transcription Regulation
Negative supercoiling profoundly affects gene expression:
- Promoter melting: (−) supercoiling lowers energy barrier for strand separation
- Supercoiling-sensitive genes: Many genes require σ ≈ −0.06 for optimal expression
- Gyrase inhibition: Quinolones rapidly shut down transcription globally
- Environmental response: Osmotic stress, temperature changes alter supercoiling
Chromatin and Nucleosomes
Eukaryotic chromatin structure is intimately connected to topology:
Nucleosome Wrapping
- • 147 bp wrapped ~1.65 turns
- • Left-handed toroidal supercoil
- • Each nucleosome: ΔLk ≈ −1
- • Constrains (−) supercoils
Topological Domains
- • TADs (topologically associating domains)
- • CTCF/cohesin boundaries
- • Insulate supercoiling effects
- • Regulate enhancer-promoter contacts
Disease Connections
Cancer
Topo II poisons (etoposide, doxorubicin) are chemotherapy drugs. Therapy-related leukemia from Topo II-mediated translocations.
Neurodegeneration
Topo I defects cause spinocerebellar ataxia. TOP3B mutations linked to schizophrenia and cognitive disorders.
Development
Cohesinopathies (Cornelia de Lange syndrome) affect topological domain organization.
Experimental Methods
Gel Electrophoresis
- Principle: Supercoiled DNA migrates faster than relaxed
- Topoisomers: Different Lk values appear as ladder
- Chloroquine gels: Intercalator shifts mobility pattern
- 2D gels: Resolve complex topological mixtures
Single-Molecule Methods
- Magnetic tweezers: Rotate DNA, measure extension vs. turns
- Optical tweezers: Apply force, monitor supercoiling transitions
- AFM: Visualize plectonemes and knots directly
- FRET: Monitor topology changes in real time
Psoralen Crosslinking
- Principle: Psoralen intercalates preferentially in (−) supercoiled DNA
- UV crosslink: Creates covalent link between strands
- Quantification: More crosslinks = more (−) supercoiling
- Mapping: Identify supercoiled regions genome-wide
GapR-seq / Topo-seq
- GapR: Protein that binds (+) supercoiled DNA
- ChIP-seq: Map (+) supercoiling genome-wide
- Topo-seq: Map topoisomerase cleavage sites
- Resolution: ~100-1000 bp regions
Key Equations Summary
Linking number equation
Relaxed linking number
Linking number deficit
Superhelical density
Key Takeaways
- ✓ DNA topology describes how DNA strands are interlinked and how the helix coils in space
- ✓ Lk = Tw + Wr: Linking number equals twist plus writhe (fundamental topological constraint)
- ✓ Cellular DNA is negatively supercoiled (σ ≈ −0.06), facilitating strand separation
- ✓ Type I topoisomerases cut one strand, change Lk by ±1, no ATP required
- ✓ Type II topoisomerases cut both strands, change Lk by ±2, require ATP
- ✓ DNA gyrase uniquely introduces (−) supercoils; essential for bacteria, antibiotic target
- ✓ Topological problems (catenanes, knots) must be resolved for chromosome segregation
- ✓ Nucleosome wrapping constrains (−) supercoils in eukaryotic chromatin