Ramachandran plot

A Ramachandran plot (also known as a Ramachandran Map or a Ramachandran diagram) 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.

Structure

Below are the backbone dihedral angles φ and ψ referred to throughout this article:

Phi/Psi and Residue Type

Residues in Ramachandran plots are usually sorted into four separate types:

• General (not Proline, not Glycine, not before a Proline)
• Glycine (the small side chain makes the protein backbone very flexible)
• Proline (their large side chain restricts backbone movement)
• Pre-Proline (proline even messed up any residue before it)

Lovell, et al. Definition

"As the number of protein structures that have been solved has increased, our knowledge concerning the empirical distribution of phi/psi angles in proteins has improved. In 2003, Lovell and coworkers published updated definitions of the 'Preferred' and 'Allowed but Disfavoured' regions of the Ramachandran plot. Nearly 100,000 residues from 500 structures with resolution better than or equal to 1.8 Angstroms were used to define the empirical distribution."—Peter N. Robinson

Geometrical validation around the Calpha is described, with a new Cbeta measure and updated Ramachandran plot. Deviation of the observed Cbeta atom from ideal position provides a single measure encapsulating the major structure-validation information contained in bond angle distortions. Cbeta deviation is sensitive to incompatibilities between sidechain and backbone caused by misfit conformations or inappropriate refinement restraints. A new phi,psi plot using density-dependent smoothing for 81,234 non-Gly, non-Pro, and non-prePro residues with B < 30 from 500 high-resolution proteins shows sharp boundaries at critical edges and clear delineation between large empty areas and regions that are allowed but disfavoured. One such region is the gamma-turn conformation near +75 degrees,-60 degrees, counted as forbidden by common structure-validation programs; however, it occurs in well-ordered parts of good structures, it is overrepresented near functional sites, and strain is partly compensated by the gamma-turn H-bond. Favoured and allowed phi,psi regions are also defined for Pro, pre-Pro, and Gly (important because Gly phi,psi angles are more permissive but less accurately determined). Details of these accurate empirical distributions are poorly predicted by previous theoretical calculations, including a region left of alpha-helix, which rates as favourable in energy yet rarely occurs. A proposed factor explaining this discrepancy is that crowding of the two-peptide NHs permits donating only a single H-bond. New calculations by Hu et al. [Proteins 2002 (this issue)] for Ala and Gly dipeptides, using mixed quantum mechanics and molecular mechanics, fit our nonrepetitive data in excellent detail. To run our geometrical evaluations on a user-uploaded file, see MOLPROBITY (http://kinemage.biochem.duke.edu) or RAMPAGE (http://www-cryst.bioc.cam.ac.uk/rampage).

• Source: Lovell, et al.

Kleywegt and Jones Definition

"A classic definition of the core areas of the Ramachandran plot is described by Kleywegt and Jones. This definition divides the phi/psi space into two regions: Core and noncore. The core regions are given by the 10° x 10° regions that together account for 98% of all non-glycine residues in a large sample of protein structures."—Peter N. Robinson

This week's unusual Ramachandran plots

Every week, Kleywegt and Jones (after updating their local copy of the PDB) check the Ramachandran plots of all protein chains. All chains that have 20 or more residues, and of which at least 10% are outliers are listed in this file: http://xray.bmc.uu.se/gerard/rama/ramathisweek.txt (Note that this list may include NMR and theoretical models.)

Structural motifs/features

Note: Eventually, each of these motifs/features will have their own section with explanations, data, and examples.

• Beta turns
• Beta strands
• Beta bulges
• Beta hairpins
• Beta alpha beta units
• Beta sheet topology
• Disulphide bridges
• Gamma turns
• Helical geometry
• Helical interactions
• Main chain hydrogen bonding patterns
• Psi loops
• Secondary structure

Beta turns

Reverse turns are a common feature of protein structures that allow a significant change in the direction of the polypeptide chain. So-called beta turns are a well-studied subset of reverse turns.

The standard criteria for defining a beta turn are that a beta turn comprises four amino acid residues, whereby the distance between the first and the last alpha carbon is less than 7 Ångströms and the central two residues are not helical. Eight conventional turn types (I,I',II,II',VIa, VIb, VIII, and other) are defined according to the phi (φ) and psi (ψ) torsion angles of the second and third residues.

Table 1: Beta turn types
Type	φ(i+1)	ψ(i+1)	φ(i+2)	ψ(i+2)
I	-60°	-30°	-90°	0°
I'	60°	30°	90°	0°
II	-60°	120°	80°	0°
II'	60°	-120°	-80°	0°
VIa	-60°	120°	-90°	0°
VIb	-120°	120°	-60°	0°
VIII	-60°	-30°	-120°	120°

Source: Wilmot, et al.

Tetrapeptide conformations and solvent effects

Note: The following section is for the tetrapeptide, HCO-L-Ala-L-Pro-Gly-Gly-OMe.

         φ1     φ1         φ2    φ2         φ3    φ3         φ4     φ4
HCO----N----Ca----C'----N----Ca----C'----N----Ca----C'----N----Ca----C'----O----CH3
            Ala1             Pro2             Gly3             Gly4

The Table 2 uses CNDO/2 molecular orbital total energies in kcal/mole, molecular dipole moments in Debyes, and expose molecular surface areas in Ų.

Table 2: Beta turn types and energies
Conformation	φi	ψi	φi+1	ψi+1	φi+2	ψi+2	φi+3	ψi+3	CNDO/2 Total Energy	Molecular Dipole Moment	Exposed Molecular Surface Area
1: Type II β-turn and 14-membered H-bonded conformation	-90°	150°	-60°	130°	90°	40°	-170°	130°	-171,145.25	5.17	362.96
2: Type I β-turn and 14-membered H-bonded conformation	-120°	150°	-60°	-30°	-90°	0°	±180°	90°	-171,134.25	5.25	367.01
3: Type II β-turn	-100°	-20°	-60°	120°	80°	0°	70°	±180°	-171,135.31	13.30	368.45
4: Type II β-turn	50°	140°	-60°	120°	80°	0°	70°	±180°	-171,120.13	13.82	357.07
5: Type I β-turn	-100°	-20°	-60°	-30°	-90°	0°	70°	±180°	-171,127.50	13.23	367.36

Source: Renugopalakrishnan, et al.

where,

1. Prefered in vacuo conformation of HCO-APGG-OMe with a type II β-turn between Ala₁ C=O and Gly₄ NH and a 14-membered H-bonded ring between Gly₄ C=O and Ala₁ NH.
2. A type I β-turn conformation stabilized by a 14-membered H-bond ring as in 1 above with the torsion angles given in Table 2.
3. A type II β-turn conformation with φ₁ = -100° and ψ₁ = -20° for Ala₁ residue where the 14-membered H-bond is absent. Gly₄ residue was fixed at an energetically favourable conformation with φ₄ = 50° and ψ₄ = ±180°.
4. A type II β-turn conformation with φ₁ = 50° and ψ₁ = 140° for Ala₁ residue where the 14-membered H-bond is absent. The Gly₄ residue was fixed at the same energetically favourable conformation as in 3 above.
5. A type I β-turn conformation with φ₁ = -100° and ψ₁ = -20° for Ala₁ residue where the 14-membered H-bond is absent. The Gly₄ residue was fixed at the same energetically favourable conformation as in 3 above.

"A tetrapeptide can be classified into one of the above types if all four angles fall within 30° of the 'ideal' angles given in the table. Beta turns not fulfilling the requirements for one of the above turns are classified as 'other'. Many unclassifiable turns represent distortions of the the conventional turn types, lying just outside the standard limits. Therefore, the same authors showed that it is possible to increase the number of classifiable turns by allowing one of the four angles to deviate by as much as 45°."—Peter N. Robinson

Disulphide Bridges

Disulphide bridges are identified for two cysteine residues whose sulphur atoms are less than 3 Angstroms apart. Richardson (1981) identified several categories of disulphide bridges based on their internal chi angles, in particular the chi2, chi3 and chi2' angles.

Table 3: Disulphide bridge categories
Disulphide type	χ2	χ3	χ2'
left handed spiral	-	-	-
right handed hook	+	+	-
right handed spiral	+	+	+
short right handed hook	-	+	-

Source: Richardson (1981)

Note that the chi2 and chi2' values can be interchanged, as they merely reflect which of the two cysteines involved in the bridge is mentioned first. If the other cysteine were mentioned first the chi and chi' values would be interchanged.

Richardson found that the majority of disulphides could be classed as left handed spirals or right handed hooks.

Gamma turns

A Gamma turn is defined for 3 residues i, i+1, i+2 if a hydrogen bond exists between residues i and i+2 and the phi and psi angles of residue i+1 fall within 40 degrees of one of the following 2 classes:

Table 4: Gamma turn angles
Turn type	φi+1	ψi+1
classic	75.0	-64.0
inverse	-79.0	69.0

Sources: Milner-White, et al. 1981 and Rose, et al. 1985

Calculation of E_solute

E_solute represents the intrinsic intramolecular interactions and is calculated using partitioned potential energy functions. E_solute consists of four terms:

1. van der Waals interaction energy;
2. electrostatic interaction energy;
3. torsional energy across N—C^α, C^α—C', and C^α—C^β bonds. Proline side chains are assumed to remain in a fixed geometry; and
4. hydrogen-bonding energy.

Dihedral angles of biological molecules

The backbone dihedral angles of proteins are called φ (involving the backbone atoms C'-N-Cα-C'), ψ (involving the backbone atoms N-Cα-C'-N) and ω (involving the backbone atoms Cα-C'-N-Cα). Thus, φ controls the C'-C' distance, ψ controls the N-N distance and ω controls the Cα-Cα distance.

The planarity of the peptide bond usually restricts ω to be 180° (the typical trans case) or 0° (the rare cis case). The distance between the Cα atoms in the trans and cis isomers is approximately 3.8 and 2.8 Å, respectively. The cis isomer is mainly observed in X-Pro peptide bonds (where X is any amino acid).

The sidechain dihedral angles of proteins are denoted as χ1-χ5, depending on the distance up the sidechain. The χ1 dihedral angle is defined by atoms N-Cα-Cβ-Cγ, the χ2 dihedral angle is defined by atoms Cα-Cβ-Cγ-Cδ, and so on.

The sidechain dihedral angles tend to cluster near 180°, 60°, and -60°, which are called the trans, gauche+, and gauche- conformations. The choice of sidechain dihedral angles is affected by the neighbouring backbone and sidechain dihedrals; for example, the gauche+ conformation is rarely followed by the gauche+ conformation (and vice versa) because of the increased likelihood of atomic collisions.

Dihedral angles have also been defined by the IUPAC for other molecules, such as the nucleic acids (DNA and RNA) and for polysaccharides.

References

See also

• MolProbity
• RAMPAGE
• Rotamer tables — rotamer parameters used in the rotamer program (in ccp4)

External links

• Richardson Lab and Kinemage homepage
  • Ramachandran Redux
• Calculating Ramachandran (phi/psi) Angles — by Peter Cock
• Drawing Ramachandran (phi/psi) plots for Proteins with R — by Peter Cock
• AAindex — Amino acid indices and similarity matrices
• A Java Program For Drawing Ramachandran Plots
• wikipedia:Ramachandran plot