Q7(b). Length of an α-helix and of B-DNA; effect of denaturation

Introduction. Both are helices whose length is set by the rise per unit along the axis. An α-helix has 3.6 residues per turn and a pitch of 5.4 Å, i.e. a rise of 1.5 Å per residue. B-DNA has 10 base pairs per turn and a rise of 3.4 Å per base pair.

Given: n = 74 residues or base pairs; rise 5.4/3.6 = 1.5 Å per residue (α-helix); 3.4 Å per base pair (B-DNA).

L_α=74×1.5 Å=111 Å=11.1 nm L_(DNA)=74×3.4 Å=251.6 Å≈25.2 nm

L_DNA/L_α = 3.4/1.5 ≈ 2.27

Figure: Same number of units: the DNA double helix is about 2.3 times longer.

1. Comparison. The α-helix (20.6 turns) is a compact coil, 11.1 nm long; B-DNA with the same number of units (7.4 turns) is about 2.3 times longer, 25.2 nm, because the stacked base pairs are 3.4 Å apart while amino acid residues advance only 1.5 Å.
2. Protein on denaturation: length increases. Heat, urea or extreme pH breaks the intrachain C=O…H–N hydrogen bonds (between residues i and i+4). The helix unwinds into an extended chain in which consecutive residues are up to 3.5 Å apart, so the contour length can rise from 111 Å to about 259 Å (74 × 3.5 Å).
3. DNA on denaturation: length decreases. Heating above the melting temperature breaks the interstrand base-pair hydrogen bonds and base stacking; the two strands separate (hyperchromic effect in the UV). The rigid, rod-like 25 nm duplex is replaced by two flexible single strands that collapse into random coils, whose end-to-end length is much shorter.

Conclusion. α-helix (74 residues) = 111 Å (11.1 nm); B-DNA (74 bp) = 251.6 Å (25.2 nm), about 2.3 times longer. On denaturation the polypeptide lengthens (helix → extended chain, up to 3.5 Å per residue), while DNA shortens (rigid duplex → coiled single strands).

Application. These dimensions explain why a protein helix of about 20 residues (3 nm) just spans a cell membrane and why the double helix packs 3.4 Å per base pair into chromatin; DNA melting curves are used to measure GC content.