Ramachandran Plots

The Ramachandran plot is a fundamental tool for understanding and validating protein backbone conformations.

Backbone Dihedral Angles

The protein backbone consists of a repeating sequence of N, Cα, and C atoms. The conformation of each residue is primarily determined by two dihedral (torsion) angles:

Phi (φ): Rotation about the N–Cα bond.
Psi (ψ): Rotation about the Cα–C bond.
Omega (ω): Rotation about the C–N (peptide) bond. This is typically fixed near 180° (trans) or 0° (cis).

Theoretical Basis

A Ramachandran plot (φ vs. ψ) displays the energetically allowed regions for backbone dihedral angles. Some combinations of φ and ψ are prohibited due to steric clashes between the carbonyl oxygen (O) and the amide hydrogen (H), or between the side-chain atoms and the backbone.

Allowed Regions

Alpha-Helix: φ ≈ -57°, ψ ≈ -47°.
Beta-Sheet: φ ≈ -135°, ψ ≈ 135°.
Polyproline II (PPII): φ ≈ -75°, ψ ≈ 145°.

Implementation in `synth-pdb`

synth-pdb uses Ramachandran principles in two ways:

Structure Generation: When using the --conformation or --structure flags, the tool uses preset φ and ψ angles (defined in synth_pdb/data.py) to build the backbone.
Validation: The --validate flag calculates the φ and ψ angles of the generated structure and checks if they fall within the allowed regions.

Presets

Conformation	Phi (°)	Psi (°)
`alpha`	-57.0	-47.0
`beta`	-135.0	135.0
`ppii`	-75.0	145.0
`extended`	-120.0	120.0

Special Cases

Glycine (GLY): Lacks a side chain, so it has much more conformational freedom. Its Ramachandran plot is broader and more symmetric.
Proline (PRO): Its side chain is cyclized back to the backbone Nitrogen, making it the most restricted residue. It is often a "structure breaker."
Cis-Proline: Proline is unique in having a relatively high frequency (~5%) of the cis peptide bond (ω ≈ 0°), which synth-pdb can simulate via the --cis-proline-frequency flag.