Ramachandran Plot

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The Ramachandran plot is a plot of the torsional angles - phi (φ)and psi (ψ) - of the residues (amino acids) contained in a peptide. In sequence order, φ is the N(i-1),C(i),Ca(i),N(i) torsion angle and ψ is the C(i),Ca(i),N(i),C(i+1) torsion angle. The plot was developed in 1963 by G. N. Ramachandran, et. al.^[1] by plotting the φ values on the x-axis and the ψ values on the y-axis, as for the image at left^[2]. Plotting the torsional angles in this way graphically shows which combination of angles are possible. The torsional angles of each residue in a peptide define the geometry of its attachment to its two adjacent residues by positioning its planar peptide bond relative to the two adjacent planar peptide bonds, thereby the torsional angles determine the conformation of the residues and the peptide. Many of the angle combinations, and therefore the conformations of residues, are not possible because of steric hindrance. By making a Ramachandran plot, protein structural scientists can determine which torsional angles are permitted and can obtain insight into the structure of peptides. The scene on the right is the Ramachandran plot of ribonuclease H.

Contents 1 Secondary structure plot regions 1.1 α-helix 1.2 β-sheets 2 Plot regions limited by steric hindrance 2.1 Glycine, Proline, etc. 2.2 Functionally relevant residues 3 Plots of proteins

Secondary structure plot regions

Secondary structures of a peptide are segments of the peptide that have ordered and repetitive structure, and the repetitive structure is due to a repetitive conformation of the residues and, ultimately, repetitive values of φ and ψ. The different secondary structures can be distinguished by their range of φ and ψ values with the values of different secondary structures mapping to different regions of the Ramachandran plot. Two common examples of secondary structure are illustrated below.

α-helix

The shows the axis of the α-helix rotating in the y-plane. When viewing the helix on end, observe the open center of the helix. are drawn on some of the peptide bonds to emphasize that in an α-helix the planar peptide bonds rotate about the axis of the helix. The of this peptide has points clustered about the values of φ= -57^o and ψ= -47^o which are the average values for α-helices. of two other helical segments demonstrates that data from all three appear in one large cluster and that the helical segments can not be distinguished by the differences in their φ and ψ values.

β-sheets

a two segment twisted β-sheet. of the peptide bonds. Most β-sheets in globular proteins are twisted sheets which do not have flat parallel pleats. of β-sheets. The of this twisted sheet has points clustered about the values of φ= -130^o and ψ= +140^o which are the average values for twisted sheets. of three other sheet segments more clearly defines the area in which values for twisted sheets are located.

Plot regions limited by steric hindrance

Most combinations of φ and ψ are sterically forbidden, , Glu-Ser-Ala. With Ser having values of φ = 55^o and ψ = -116^o the Ser side chain is in contact with the Ala, colored blue. In plots of native peptides the data points will form clusters in the several areas in which steric hindrance does not occur. These regions are illustrated in the Figure on the left, according to our understanding in the early 1990's when the first validation programs such as ProCheck^[3] were developed The core regions (blue in the Figure) contain the most favorable combinations of φ and ψ and contain the greatest number of points. Plots of some proteins contain a small third core region in the upper right quadrant. The allowed regions (green in the Figure) can be located around the core regions or can be unassociated with a core region, but they contain fewer data points than the core regions. The generous regions (not shown in the Figure) extend beyond the allowed regions. The remaining areas are considered disallowed. Observe that the data point 55^o, -116^o for Ser of the above tripeptide would fall in the lower right quadrant which contains only a disallowed region in ProCheck. If the Ser in the tripeptide has φ and ψ values of -57^o and -47^o which are in the core region in the lower left, the is rotated away from the Ala and is not in contact with the Ala. Most, if not all, of the points in the above plots for α-helix and β-sheet are in one of the core areas.

Since the 1990's, great expansion in the number and quality of macromolecular crystal structures and advances in methodology have greatly improved understanding of the energetically favored, allowed, and truly disallowed conformations of proteins and nucleic acids. The lower figure plots Ramachandran values for over a million general-case residues with resolution <2.0Å and backbone B-factor <30. Over half the plot is entirely empty, but there are further clusters evident that have moderate population and presumably have somewhat unfavorable energy but are possible; this actually includes the region near +55, -116, which is found in one type of beta turn.

Glycine, Proline, etc.

Since Gly has only a hydrogen as a side chain, steric hindrance is not as likely to occur as φ and ψ are rotated through a series of values. The with Gly having φ and ψ values of +55^o and -116^o respectively, does not show the steric hindrance that the Glu-Ser-Ala had. For that reason Gly will frequently plot in the disallowed region of a general-case Ramachandran plot. Nearly all of the data points in the disallowed region in the above Figure are Gly points. Therefore modern Ramachandran criteria^[4][5] use separate functions for subsets of the amino acids that have different local steric-hindrance properties, and may even consider the effects of sequence neighbors^[6]. Proline, with the sidechain covalently linked to the preceding backbone N, is more tightly constrained than general-case residues. Residues just before a Pro (called "prePro") have some limits from steric interaction with the proline ring. The branched beta-carbons of Ile and Val also give them a distinct shape of disallowed Ramachandran regions. The other 16 amino-acid types vary in their preference for the very favorable regions, but their outer contours that separate allowed from outlier regions all agree very closely, so they are all grouped together into the "general-case" distribution (as shown above) for structure validation purposes. The figure below shows the plots for Gly and for trans Pro (cis Pro is slightly shifted up and left, and lacks the small central cluster).

Functionally relevant residues

Functionally relevant residues are more likely than others to have torsion angles that plot to the allowed but disfavored regions of a Ramachandran plot. The specific geometry of these functionally relevant residues, while somewhat energetically unfavorable, may be important for the protein's function, catalytic or otherwise. Such conformations need to be stabilized by the protein using H-bonds, steric packing, or other means, and should very seldom occur for highly solvent-exposed residues.

Plots of proteins

Myoglobin

 : Secondary structure consists of α-helix, loops and ordered, nonrepetitive structures.

: Red data points outside of the area expected for α-helix most likely involve residues at the end of the α-helix because often these have angle values that are not typical for α-helix. White points are those for loops and ordered, nonrepetitive structures. The few residues that map to the disallowed region are Gly.

after viewing plot

Concanavalin A

: Twisted β-sheet with small segments of α-helix.

: Most of the yellow points are located in the area for twisted β-sheets where one would expect them, and again the points in the disallowed region are Gly.

after viewing plot.

Acetylcholinesterase

: Close to equal amounts of α-helix, β-sheet, and ordered, nonrepetitive structures. One important exception to Gly in the disallowed region is Ser:200. Locate this residue that is located in a disallowed region (lower right quadrant). An interesting aspect concerning Ser:200 is that it is one of a triad of residues that are part of the catalytic site and are involved in the catalytic action of this enzyme. The unique φ and ψ values for Ser:200 is the major factor in positioning the side chain so that it can participate in the catalysis.

after viewing plot.