A protein backbone is a chain of rigid, near-planar peptide units connected at the Cα carbons. Bond lengths and bond angles barely vary (N–Cα 1.46 Å, Cα–C 1.52 Å, C–N 1.33 Å; the peptide bond itself is locked near ω = 180° by partial C–N double-bond character), so almost all of a protein's 3D shape comes from just two rotatable dihedral angles per residue:
φ (phi) = dihedral( C(i-1) – N(i) – Cα(i) – C(i) )
ψ (psi) = dihedral( N(i) – Cα(i) – C(i) – N(i+1) )
This simulator places every backbone atom with the NeRF (natural extension reference frame) construction: each new atom is dropped at a fixed bond length and bond angle from the last two, then rotated to the requested dihedral — exactly the internal-coordinate method structural biology tools use to build a 3D chain from a φ/ψ table.
Not every (φ,ψ) pair is possible — many collide the carbonyl oxygen or amide hydrogen with a neighboring atom. Ramachandran (1963) mapped the sterically allowed combinations; this plot's shaded regions mark the three empirically dense basins:
- α-helix — φ≈-60°, ψ≈-45°, a right-handed helix stabilized by i→i+4 hydrogen bonds.
- β-sheet — φ≈-120°, ψ≈+120°, the near-extended strand conformation.
- Left-handed αL / PPII — smaller basins, common for glycine and collagen-like chains.
Drag φ/ψ for the selected residue, or apply a preset to the whole chain, and watch the 3D backbone refold live. Pushing φ/ψ into the white "disallowed" zone drives real backbone atoms within clash range of each other — the simulator flags this by measuring every non-bonded atom pair and turning offending atoms red.