Dihedral/Dihedral angles in proteins

The model displayed on the right is a tripeptide (Trp₃₄–Glu₃₅–Ser₃₆ within the protein lysozyme). This page illustrates the meaning of phi (ϕ) and psi (ψ) angles, both around the alpha carbon of the central residue (Glu₃₅). Both are dihedral angles, meaning an angle formed between two planes (as compared to regular angles, formed between two lines or bonds). They are also called torsion angles, meaning the torsion or rotation around a bond.

phi (ϕ) is the angle between these two planes:

• plane defined by C_i−1, N_i and C^α_i
  displayed as (1)
• plane defined by N_i, C^α_i and C_i
  displayed as (2)

Therefore ϕ means rotation around the N—C^α bond.

psi (ψ) is the angle between these two planes:

• plane defined by N_i, C^α_i and C_i
  displayed as (3)
• plane defined by C^α_i, C_i and N_i+1
  displayed as (4)

Therefore ψ means rotation around the C^α—C bond.

Note that planes 2 and 3 coincide.

In all these, "C" means the carboxylic carbon, forming the amide or peptide bond with the N. Peptide bonds are displayed in black.

You can run animations that continuously rotate the model changing one of the angles.

First, select one of the angles:

After the model has loaded,

Clashes: magenta cylinders are displayed where neighbour atoms collide (hence there is an unfavourable conformation for those particular ϕ, ψ values).