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# Ramachandran plot

A Ramachandran plot (also known as a Ramachandran map or a Ramachandran diagram), developed by Gopalasamudram Narayana Ramachandran, is a way to visualize dihedral angles φ against ψ of amino acid residues in protein structure. It shows the possible conformations of φ and ψ angles for a polypeptide.

Mathematically, the Ramachandran plot is the visualization of a function $f: \left[-\pi,\pi\right) \times \left[-\pi,\pi\right) \rightarrow \mathbb{R_{{}+{}}}$. The domain of this function is the torus. Hence, the conventional Ramachandran plot is a projection of the torus on the plane, resulting in a distorted view and the presence of discontinuities.

One would expect that larger side chains would result in more restrictions and consequently a smaller allowable region in the Ramachandran plot. In practice this does not appear the case; only the methylene group at the β position has an influence.

Glycine has a hydrogen atom, with a smaller van der Waals radius, instead of a methyl group at the β position. Hence it is least restricted and this is apparent in the Ramachandran plot for Glycine for which the allowable area is considerably larger.

In contrast, the Ramachandran plot for proline shows only a very limited number of possible combinations of ψ and φ.

One can also plot the dihedral angles in polysaccharides in this fashion.

## Software

• STING
• Pymol with the DynoPlot extension
• VMD, distributed with dynamic Ramachandran plot plugin
• Sirius
• Swiss PDB Viewer

## References

• G.N. Ramachandran, C. Ramakrishnan & V. Sasisekharan (1963): Stereochemistry of polypeptide chain configurations. In: J. Mol. Biol. vol. 7, p. 95-99. PMID 13990617