The alpha carbon (Cα) in the center of each amino acid is held in the main chain by two rotatable bonds. The dihedral (torsion) angles of these bonds are called Phi and Psi (in Greek letters, φ and ψ). In fact, most Phi and Psi angle combinations are impossible because two atoms cannot occupy the same space. Torsion angles are dihedral angles, which are defined by 4 points in space. In proteins the two torsion angles φ and ψ describe the rotation of the polypeptide chain around the two bonds on both sides of the Cα atom.
In a polypeptide the main chain N-C alpha and C alpha-C bonds are relatively free to rotate. These rotations are represented by the torsion angles phi and psi, respectively.
Two torsion angles in the polypeptide chain, also called Ramachandran angles, after the Indian physicist who worked on modeling the interactions in polypeptide chains, G.N. Ramachandran described the rotations of the polypeptide backbone around the bonds between N-Cα (called Phi, φ) and Cα-C (called Psi, ψ). A special way for plotting protein torsion angles was also introduced by Ramachandran and co-authors, and was subsequently named the Ramachandran plot. The Ramachandran plot provides a convenient way to view the distribution of torsion angles in a protein structure. It also provides an overview of excluded regions that show which rotations of the polypeptide are not allowed due to steric hindrance (collisions between atoms). The Ramachandran plot of a particular protein may also serve as an important indicator of the quality of its three-dimensional structures.
Torsion angles are among the most important local structural parameters that control protein folding – if we would have a way to predict the Ramachandran angles for a particular protein, we would be able to predict its fold. The torsion angles phi and psi provide the flexibility required for the polypeptide backbone to adopt a certain fold, since the third possible torsion angle within the protein backbone (called omega, ω) is essentially flat and fixed to 180 degrees. This is due to the partial double-bond character of the peptide bond, which restricts rotation around the C-N bond, placing two successive α-carbons and C, O, N and H between them in one plane. Thus, rotation of the protein chain can be described as rotation of the peptide bond planes relative to each other.
G N Ramachandran used computer models of small polypeptides to systematically vary phi and psi with the objective of finding stable conformations. For each conformation, the structure was examined for close contacts between atoms. Atoms were treated as hard spheres with dimensions corresponding to their van der Waals radii. Therefore, phi and psi angles which cause spheres to collide correspond to sterically disallowed conformations of the polypeptide backbone. In the plot, the horizontal axis shows φ values, while the vertical shows ψ values. Each dot on the plot shows the angles for an amino acid. The counting starts in the left hand corner from -180 and extends to +180 for both the vertical and horizontal axes. This is a convenient presentation and allows clear distinction of the characteristic regions of α-helices and β-sheets. The regions on the plot with the highest density of dots are the so-called “allowed” regions, also called low-energy regions. Some values of φ and ψ are forbidden since they will bring the atoms too close to each other, resulting in a so-called steric clash. For a high-quality and high resolution experimental structure these regions are usually empty or almost empty – very few amino acid residues in proteins have their torsion angles within these regions.