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Ramachandran Plot

The Ramachandran plot is a plot used to study proteins. The discussions made in the dihedral angles can be used to study the structure of protein and can be graphically plotted. This was for the first time realized and mathematically analyzed by the Indian scientist, G.N. Ramachandran. Every polypeptide structure can be fully defined by its characteristic pair of Φ and Ψ angles, the backbone conformation of any particular residue in a protein can be represented as a point on a plot of Φ versus Ψ angles. Such plots are called Ramachandran plots because G. N. Ramachandran was the first to make extensive use of these plots to analyze the structure of proteins.

To understand the Ramachandran Plot let us first recall the direction of rotations about the Φ and Ψ angles. The reference point is always considered an imaginary conformation where Φ and Ψ angles are taken to be zero and both the peptide planes connected to a common Cα atom lie in the same plane. On looking from the Cα in either direction, clockwise rotations are considered positive and accordingly the Φ and Ψ dihedral angles will have a positive signs. Similarly, an anti-clockwise rotation would assign negative values to the two angles. It is thus evident and clearly discussed previously that if both the dihedral (Φ and Ψ) angles are assigned a value of +180° each, the polypeptide chain would acquire a fully extended conformation (Figure below). If, on the other side, the two angles are assigned a value of 0° each, the two successive peptide planes would become co-planar and come closer to each other to the extent that the carbonyl oxygen and amino hydrogen would sterically clash. It is therefore conceivable that not all possible structural conformations will ever become a reality.

Some features of a typical Ramachandran plots are shown below in figure. Clearly, well known secondary structures (described below) of proteins have a tendency of acquiring only certain “allowed” values of the two dihedral angles. A major area of the plot is represented by such combinations of Φ and Ψ angles which are “disallowed” while limited regions may also be “partially allowed” conformational zones.

Therefore, the Ramachandran plot of a protein is a full description of the polypeptide backbone conformation (side chain conformations can be excluded). Three important regions of the Ramachandran plot describe the most commonly found secondary structures in proteins:

α -helix: a right handed helical structure with average torsion angles Φ =-57° &  Ψ =-47°.

β -sheet: parallel (Φ =-119° and Ψ =113°) or anti-parallel pleated sheet structures.

β -turn: minimal loop structures of 3 to 4 amino acids with defined torsion angles. 

In the diagram below the unshaded areas correspond to conformations where atoms in the polypeptide come closer than the sum of their van der Waals radii. These regions are sterically disallowed (/forbidden) for all amino acids except glycine which is unique in that it lacks a side chain. The dark shaded regions correspond to conformations where there are no steric clashes, i.e., these are the allowed regions namely the alpha-helical and beta-sheet conformations. The lighter shaded areas show the partially allowed regions if slightly shorter van der Waals radi are used in the calculation, i.e., the atoms are allowed to come a little closer together. This brings out an additional region which corresponds to the left-handed alpha-helix.

Ramachandran diagram showing the sterically reasonable values of the angles Φ and ψ. The shaded regions indicate particularly favorable values of these angles. Adapted ( (Biochemistry | 4th Edition, Christopher K Mathews )

Some values of Φ and Ψ are not allowed due to steric interference between nonbonded atoms and they are:

  •  Values Φ = 0° and Ψ = 180° are forbidden because of unfavorable overlap between the carbonyl oxygens (Figure a).
  •  Values of Φ =   180° and Ψ = 0° are not allowed because of the forbidden overlap of the N–H hydrogens (Figure b).
  •  Values Φ = 0° and Ψ = 0°are forbidden because of unfavorable overlap between the carbonyl oxygen and N–H hydrogens (Figure c).
  •  While, values of Φ =180° and Ψ = 180° generate fully extended polypeptide chain (Figure d).
A Many of the possible conformations about an α -carbon between two peptide planes are forbidden because of steric crowding.