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 Incoming links: Pi helix

Past exam of the chemistry B course of the University of Cambridge / 2025 / Paper 1 / B5 / d / Solution 2026-10-20

i

accepting from the NH of a later residue, the possibilities are:

$i \to i + 1$ : a very small four-membered hydrogen-bonded loop, incompatible with a favourable repeating peptide-backbone geometry.
$i \to i + 2$ : a seven-membered loop associated with a gamma turn; a long regular two-residue-per-turn structure is strongly constrained.
$i \to i + 3$ : the ten-membered hydrogen-bonded rings of a 3-10 helix, with about three residues per turn.
$i \to i + 4$ : the thirteen-membered rings of an alpha helix, with about 3.6 residues per turn.
$i \to i + 5$ : the sixteen-membered rings of a pi helix, with about 4.4 residues per turn.

Figure 1.
Top-view side-chain directions in 3-10, alpha and pi helices
. **Details**.

The alpha helix provides a favourable combination of allowed backbone torsions, reasonably linear hydrogen bonds, and side-chain packing. Its successive side chains advance by about

10 0^{\circ}

, rather than lining up in the three columns of the narrower 3-10 helix. Smaller repeating rings impose more severe backbone constraints; the wider pi helix gives a different, generally less favourable packing arrangement. Short 3-10 and pi-helical segments can still occur in proteins, so this is a preference for a common extended secondary structure, not a prohibition of the alternatives. Proline and sequence-specific interactions can disrupt the idealized backbone donor pattern.

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Pi helix 2026-10-20

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A pi helix contains carbonyl-i to NH-(i+5) hydrogen bonds, sixteen-membered hydrogen-bonded rings, and approximately 4.4 residues per turn.

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