Understanding DNA Topology: Linking Number, Twist, and Writhe
DNA topology is characterized by three key parameters: linking number (L), twist (T), and writhe (W). These quantify DNA’s spatial arrangement and are interrelated by the equation L = T + W. This relation governs supercoiling and conformational changes in DNA.
Linking Number (L)
The linking number is an integer representing the total number of times one DNA strand winds around the other in a closed double helix. It is a topological invariant in covalently closed circular DNA, meaning it cannot change without breaking DNA strands.
For linear DNA with fixed ends, L is effectively constant during normal cellular processes. Any change in DNA conformation must balance changes in twist and writhe to preserve L.
Twist (T)
Twist measures the number of helical turns of the DNA strands around the helical axis. In B-DNA, the most common form, about 10.5 base pairs comprise one complete turn.
Different DNA forms differ in T. For example, Z-DNA is left-handed and has about 12 base pairs per turn, causing a shift in twist compared to B-DNA.
Writhe (W)
Writhe reflects the DNA axis coiling in 3D space and encompasses supercoiling. It can be positive or negative and compensates for changes in twist to maintain constant linking number.
When DNA adopts Z-DNA conformation, the increased twist (T) requires a corresponding change in writhe (W) so that L = T + W remains true.
Applications and Example: B-DNA to Z-DNA Transition
- B-DNA’s typical twist is about 10.5 base pairs per turn.
- Z-DNA has left-handed helicity, with 12 base pairs per turn.
- Transition from B-DNA to Z-DNA increases twist, which without change in writhe would alter linking number, an impossibility for closed DNA.
- The DNA compensates by adopting writhe (supercoils or loops) that adjust for this twist increment.
This adjustment addresses topological stress during biological processes such as transcription and chromatin remodeling.
Summary Table: DNA Topological Parameters
| Parameter | Description | Typical Values |
|---|---|---|
| Linking Number (L) | Total times one strand winds around the other; topological constant | Integer, e.g., ~number of base pairs / 10.5 for B-DNA |
| Twist (T) | Number of helical turns of strands around axis | B-DNA: ~10.5 bp/turn; Z-DNA: ~12 bp/turn (left-handed) |
| Writhe (W) | Spatial coiling of helical axis (supercoiling) | Adjusts to maintain L; positive or negative |
Further Reading
Details on Z-DNA and differences from other DNA forms are accessible through this comprehensive resource.
Key Takeaways
- DNA topology is governed by the equation L = T + W.
- Linking number (L) is fixed for closed DNA and constrains DNA conformation.
- Twist (T) varies with DNA conformation; e.g., B-DNA vs Z-DNA differs in helical turns per base pair.
- Writhe (W) compensates twist changes to maintain constant linking number.
- Transitions from B-DNA to Z-DNA induce topological adjustments critical for DNA function.
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