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Ramachandran Plot

A graphical representation of allowed dihedral angles in protein structures, guiding the prediction of stable conformations.
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The statement of the theorem

Let ϕ\phi and ψ\psi be the dihedral angles defining the backbone conformation of an amino acid residue. The allowed conformational space is restricted by steric hindrance and local energy minima. The Ramachandran plot defines the allowed region R\mathcal{R} in the (ϕ,ψ)(\phi, \psi) plane: R={(ϕ,ψ)∈[−π,π)2∣Esteric(ϕ,ψ)<Ecutoff and Etorsion(ϕ,ψ)<Ecutoff}.\mathcal{R} = \{(\phi, \psi) \in [-\pi, \pi)^2 \mid E_{steric}(\phi, \psi) < E_{cutoff} \text{ and } E_{torsion}(\phi, \psi) < E_{cutoff} \}. The function EstericE_{steric} accounts for atomic overlaps, and EtorsionE_{torsion} accounts for backbone bond angle strain.
Source: Wikipedia