= Solution
For a <carbonyl> <oxygen> of residue $i$ 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.
\Image[/past-exam-of-the-chemistry-b-course-of-the-university-of-cambridge/2025/paper-1-helix-projections.png]
{title=Top-view side-chain directions in 3-10, alpha and pi helices}
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 $100^\circ$, 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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