CH9.2 - DNA Supercoiling Comprehensive Study Notes

Definition & Visual Analogy

• DNA supercoiling = “coiling of coils”; the duplex helix (first-order coil) further coils upon itself (second-order coil)
• Analogy: old-fashioned telephone/film cord – primary coils correspond to DNA helix; the cord twisting on itself illustrates a supercoil
• Relaxed DNA = closed circular B-form DNA with no supercoils (10.5 bp/turn)

Core Functions of Supercoiling

• Compaction: fits very long chromosomal DNA into limited cellular space (bacteria, nuclei, viral capsids)
• Accessibility: underwound DNA is easier to strand-separate, facilitating replication & transcription
• Bidirectional relationship: replication / transcription both require supercoiling (they locally unwind DNA) and simultaneously generate additional supercoiling ahead/behind moving polymerases

Mechanical Generation of Supercoils

• Rubber-band demo: two intertwined bands (duplex), one end fixed, local separation ➔ overwound (positively supercoiled) region ahead, underwound (negatively supercoiled) region behind
• RNA polymerase illustration: enzyme opening duplex imposes torsional strain that propagates as supercoils

Underwinding vs Overwinding

• Underwound DNA: fewer turns than B-form expectation ➔ negative supercoils; can be relieved by
– formation of supercoils (energetically favored over breaking H-bonds)
– local strand separation (uses more energy)
• Overwound DNA: more turns than expected ➔ positive supercoils; relieves stress by supercoiling (NOT by strand separation)

Example (84 bp circle):
• Relaxed: $\frac{84\,\text{bp}}{10.5\,\text{bp/turn}} = 8\,\text{turns}$
• If observed turns = 7 ➔ underwound ➔ negative supercoil formation

Linking Number (LK) – Topological Invariant

• Symbol: $LK$ or $L_k$
• Definition: total number of times one DNA strand crosses the other in a closed, covalently intact duplex
• Always an integer for closed circular (or constrained linear) DNA
• Visualization: treat one strand as boundary of a surface; count penetrations of the second strand through that surface (Fig. with 6 penetrations ⇒ $LK = 6$)

Reference Linking Number

• Relaxed B-form linking number: $L_k^0 = \frac{\text{bp length}}{10.5\,\text{bp/turn}}$

Change in Linking Number and Superhelical Density

• Topoisomerases (next lecture) alter $LK$ in units of ±1 or ±2
• Change: $\Delta L<em>k = L</em>k - L<em>k^0$ • Superhelical density (σ): length-independent measure $\sigma = \frac{\Delta L</em>k}{L_k^0}$
• Typical cellular range: $-0.07 \le \sigma \le -0.05$ (most DNA is mildly underwound)

Example (2100 bp circle)
• Relaxed: $L<em>k^0 = 200$ • After enzyme action: $L</em>k = 198$
• $\Delta L_k = -2$ (underwinding)
• $\sigma = \frac{-2}{200} = -0.01$

Sign Convention & Handedness

• Negative $\Delta L<em>k$ / negative σ ⇒ underwinding ⇒ negative supercoils ⇒ right-handed writhe • Positive $\Delta L</em>k$ / positive σ ⇒ overwinding ⇒ positive supercoils ⇒ left-handed writhe

Decomposition: Twist (Tw) & Writhe (Wr)

• Relationship: $LK = Tw + Wr$
– $Tw$ (twist): local helical turns;
molecularly, # times one strand crosses the other
– $Wr$ (writhe): global crossing of double-helical axes (supercoil crossings)
• Tw & Wr can interchange (conformational changes) without altering total $LK$
Examples (all with $LK = +3$):

1. $Tw = 3, \; Wr = 0$ (no supercoil)

2. $Tw = 2, \; Wr = 1$ (one right-handed supercoil)

3. $Tw = 1, \; Wr = 2$ (two supercoils)

4. $Tw = 0, \; Wr = 3$ (three supercoils)

Physical Configurations

Plectonemic Supercoils

• Interwound right-handed branches (telephone-cord style)
• Highly stable in solution
• Dominant in bacteria & plasmids; visualized by EM as intertwined loops
• Not sufficient alone for extreme compaction required in eukaryotic chromatin

Solenoidal Supercoils

• Left-handed, tightly wrapped turns resembling a garden hose
• Less stable; require stabilizing proteins (e.g., histone octamer in nucleosomes)
• Provide additional compaction – present in both bacterial nucleoid organization and eukaryotic chromatin

Biological & Practical Implications

• Underwound (negatively supercoiled) state primes DNA for quick strand separation—critical for rapid initiation of replication origins & highly transcribed promoters
• Positive supercoils accumulate ahead of polymerase; negative accumulate behind ➔ necessitates topoisomerases to remove torsional stress, maintain σ within viable limits
• Antibiotics & anticancer drugs often target topoisomerases, exploiting dependence of cells on controlled supercoiling
• Laboratory plasmid preps: supercoiled DNA migrates faster on agarose gels than relaxed or nicked forms—diagnostic for integrity

Numerical / Formula Summary

• B-form pitch: $10.5\,\text{bp/turn}$
• Lk^0 = Nbp / 10.5

• Lk = Lk0 + delta Lk

• sigma = delta Lk / delta Lk0
• Delta Lk = sigma x Lk0
• Sign: negative σ ⇒ right-handed supercoil; positive σ ⇒ left-handed supercoil
• Component relation: $LK = Tw + Wr$

Links to Previous / Future Lectures

• Previous: DNA length vs cell size → need for compaction
• Upcoming: enzymology of supercoiling (topoisomerase I/II; gyrase) required to create or relax supercoils arising during replication & transcription

Ethical / Philosophical Notes

• Drug targeting of supercoiling machinery raises questions about antibiotic resistance & selective toxicity
• Synthetic biology relies on understanding supercoil dynamics to design stable plasmids and gene circuits

Study Tips

• Memorize sign convention (negative = underwound/right-handed)
• Practice calculating $L<em>k$, $\Delta L</em>k$, and σ for circles of varying size
• Visualize Tw vs Wr swaps by sketching helices or using phone-cord models
• Relate gel electrophoresis band patterns to superhelical density in lab data