Secondary Structure & Torsion Angles

The Peptide Bond

The peptide bond has partial double-bond character due to resonance between amide resonance forms. Consequences include:

• Planarity of the peptide group: the six atoms of the amide unit (Cα-CO-N-Cα) lie in one plane.
• Restricted rotation about the C-N bond. The omega (ω) angle is near 180° for the usual trans peptide bond and near 0° for the rare cis configuration.
• Trans dominance: roughly 99.95% of peptide bonds are trans. The major exception is bonds N-terminal to proline, where cis content can reach several percent (often cited around 6%) because the cyclic side chain reduces the steric penalty of cis.

Bond lengths reflect partial double-bond character: the peptide C-N distance is about 1.33 Å, shorter than a typical aliphatic C-N single bond near 1.49 Å.

Torsion Angles: Phi and Psi

For each residue, φ (phi) is the dihedral angle about the N-Cα bond (conventionally described using atoms along C-N-Cα-C), and ψ (psi) is the dihedral about the Cα-C bond (N-Cα-C-N). These are the principal rotatable bonds in the polypeptide backbone; the peptide ω angle is largely fixed at ~180° (trans).

Not all (φ, ψ) pairs are sterically allowed: clashes between backbone atoms and side-chain atoms exclude most combinations, which is why Ramachandran plots show discrete allowed regions (covered in the next chapter).

The Alpha-Helix

The classic alpha-helix is right-handed. It contains about 3.6 residues per turn, a pitch of about 5.4 Å per turn, and a rise of about 1.5 Å per residue along the helix axis. Stabilization comes from i to i+4 hydrogen bonds between C=O_i and N-H_i+4. Typical average backbone angles are about φ ≈ -57° and ψ ≈ -47°.

Helix breakers include proline (introduces a kink; lacks backbone NH for one orientation) and, in some contexts, glycine (high flexibility can disfavor a single regular helix). Helix formers often include alanine, leucine, and methionine among the strong contributors in many statistical propensity scales.

The Beta-Sheet

Beta-strands adopt an extended conformation and align side by side into beta-sheets. Representative average angles from classic surveys include parallel sheets near φ ≈ -119°, ψ ≈ +113° and antiparallel sheets near φ ≈ -139°, ψ ≈ +135° (exact values vary by structure).

Antiparallel sheets are often more stable than parallel sheets in comparable models because hydrogen bonds can be more linear. Side chains project alternately above and below the sheet plane.

Other Secondary Structures

Beta-turns reverse chain direction over about four residues. Common types include type I and type II turns; glycine and proline appear frequently because their allowed backbone and side-chain conformations fit tight turns.

The 3₁₀ helix is tighter than the alpha-helix, with i to i+3 hydrogen bonds and three residues per turn in the ideal geometry.

The polyproline II helix (left-handed, three residues per turn) is important in collagen structure, where proline and hydroxyproline-rich repeats help form the extended left-handed helix of each chain before triple-helix assembly.