In the fully extended polypeptide chain conformation, what is the relationship between the backbone torsion angles phi (φ) and psi (ψ)?

Introduction:
The geometry of polypeptide backbones is described by torsion angles phi (φ) and psi (ψ). This question examines the idealized, fully extended conformation on a Ramachandran plot and how those angles relate to protein secondary structures and steric constraints.

Given Data / Assumptions:

• Backbone torsion angles: phi around N–Cα and psi around Cα–C.
• Peptide bond itself is planar with partial double-bond character, restricting rotation across C–N.
• Fully extended means the backbone is stretched with minimal steric clash.

Concept / Approach:
On a Ramachandran plot, an idealized fully extended conformation is represented near φ = 180° and ψ = 180°. Real proteins adopt regions close to, but not exactly at, these values due to steric and electronic constraints. Beta strands occupy extended regions (often around φ ≈ −135° and ψ ≈ +135°), but the conceptual extreme of full extension is taken as φ = ψ = 180°.

Step-by-Step Solution:

Verification / Alternative check:
High-resolution structures show beta strands with extended φ, ψ values, commonly near (−135°, +135°). The idealized limiting case uses 180°, consistent with the definition of full extension rather than a specific secondary structure motif.

Why Other Options Are Wrong:

• Do not occur in nature: extended conformations do occur (e.g., beta strands).
• Cis peptide bonds: rare; most peptide bonds are trans.
• Equivalent to a beta sheet: a sheet is a higher-order arrangement of multiple strands, not just an angle set.
• phi = psi = 0°: corresponds to a compacted, sterically unfavorable geometry.

Common Pitfalls:
Equating a single-strand conformation with the multi-strand architecture of beta sheets, or assuming cis geometry is common in backbones (it is not).

Final Answer:
phi = psi = 180°