Ramachandran plot

Introduction and early history
A Ramachandran plot (also known as a Ramachandran diagram or a [φ,ψ] plot), originally developed in 1963 by G. N. Ramachandran C. Ramakrishnan and V. Sasisekharan, is a way to visualize backbone dihedral angles ψ against φ of amino acid residues in protein structure. The figure at left illustrates the definition of the φ and ψ backbone dihedral angles (called φ and φ' by Ramachandran). The ω angle at the peptide bond is normally 180°, since the partial-double-bond character keeps the peptide planar. The figure at top right shows the allowed φ,ψ backbone conformational regions from the Ramachandran et al. 1963 and 1968 hard-sphere calculations: full radius in solid outline, reduced radius in dashed, and relaxed tau (N-Calpha-C) angle in dotted lines. Because dihedral angle values are circular and 0° is the same as 360°, the edges of the Ramachandran plot "wrap" right-to-left and bottom-to-top. For instance, the small strip of allowed values along the lower-left edge of the plot are a continuation of the large, extended-chain region at upper left.

Uses
A Ramachandran plot can be used in two somewhat different ways. One is to show in theory which values, or conformations, of the ψ and φ angles are possible for an amino-acid residue in a protein (as at top right). A second is to show the empirical distribution of datapoints observed in a single structure (as at right, here) in usage for structure validation, or else in a database of many structures (as in the lower 3 plots at left). Either case is usually shown against outlines for the theoretically favored regions.



Amino-acid preferences
One might 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 to be the case; only the methylene group at Cβ has a large influence. Glycine has only a hydrogen atom for its side chain, with a much smaller van der Waals radius than the CH3, CH2, or CH group that starts all other amino acids. Hence it is least restricted, and this is apparent in the Ramachandran plot for glycine (see Gly plot at left) for which the allowable area is considerably larger. In contrast, the Ramachandran plot for proline, with its 5-membered-ring side chain connecting Cα to backbone N, shows only a very limited number of possible combinations of ψ and φ (see Pro plot at left).

More recent updates
The first Ramachandran plot was calculated just after the first protein structure at atomic resolution was determined (myoglobin, in 1960 ), although the conclusions were based on small-molecule crystallography of short peptides. Now, many decades later, there are tens of thousands of high-resolution protein structures determined by X-ray crystallography and deposited in the Protein Data Bank (PDB). Many studies have taken advantage of this data to produce more detailed and accurate φ,ψ plots (e.g., Morris et al. 1992; Kleywegt & Jones 1996; Hooft et al. 1997; Hovmöller et al. 2002; Lovell et al. 2003 ). The three figures at left show the datapoints from a large set of high-resolution structures and contours for favored and for allowed conformational regions for the general case (all amino acids except Gly, Pro, and pre-Pro), for Gly, and for Pro. The most common regions are labeled: α for α helix, Lα for lefthanded helix, β for β-sheet, and ppII for polyproline II.

Related conventions
One can also plot the dihedral angles in polysaccharides (e.g. with CARP; ) and other polymers in this fashion. For the first two protein side-chain dihedral angles a similar plot is the Janin Plot.

Software
See also PDB for a list of similar software.
 * Ramachandran plot 2.0
 * Web-based tool showing Ramachandran plot of any PDB entry
 * MolProbity web service that produces Ramachandran plots and other validation of any PDB-format file
 * STING
 * Pymol with the DynoPlot extension
 * VMD, distributed with dynamic Ramachandran plot plugin
 * WHAT_CHECK, the stand-alone validation routines from the WHAT_IF_software
 * UCSF Chimera, found under the Model Panel.
 * Sirius
 * Swiss PDB Viewer
 * TALOS