Ramachandran plot

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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.jpg

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)

Ramachandran plot - four types.png

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.[1] 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[2]

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.[1]

Kleywegt and Jones Definition

"A classic definition of the core areas of the Ramachandran plot is described by Kleywegt and Jones.[3][4] 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[2]

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.[5]


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 Å2.

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.[6]


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.[5] 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°.[7]"—Peter N. Robinson[2]

Disulphide Bridges

Disulphide bridges are identified for two cysteine residues whose sulphur atoms are less than 3 Angstroms apart. Richardson (1981)[8] 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)[8]


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[9] and Rose, et al. 1985[10]


Calculation of Esolute

Esolute represents the intrinsic intramolecular interactions and is calculated using partitioned potential energy functions.[6] Esolute consists of four terms:

  1. van der Waals interaction energy;
  2. electrostatic interaction energy;
  3. torsional energy across N—Cα, Cα—C', and Cα—Cβ 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.

Raw data

===  favored (red) regions ====
region 1:

        -177.5 -180.0
        -177.5 -177.5
        -172.5 -177.5
        -172.5 -172.5
        -167.5 -172.5
        -167.5 -167.5
        -127.5 -167.5
        -127.5 -172.5
        -97.5 -172.5
        -97.5 -167.5
        -77.5 -167.5
        -77.5 -172.5
        -72.5 -172.5
        -72.5 -177.5
        -67.5 -177.5
        -67.5 -180.0
region 2:
        57.5 67.5
        57.5 62.5
        62.5 62.5
        62.5 57.5
        67.5 57.5
        67.5 47.5
        72.5 47.5
        77.5 32.5
        77.5 2.5
        62.5 2.5
        62.5 7.5
        57.5 7.5
        57.5 12.5
        52.5 12.5
        52.5 22.5
        47.5 22.5
        47.5 27.5
        42.5 27.5
        42.5 37.5
        37.5 37.5
        37.5 62.5
        42.5 62.5
        42.5 67.5
        57.5 67.5
region 3:
        -62.5 180.0
        -62.5 172.5
        -57.5 172.5
        -57.5 167.5
        -52.5 167.5
        -52.5 157.5
        -47.5 157.5
        -47.5 147.5
        -42.5 147.5
        -42.5 137.5
        -37.5 137.5
        -37.5 122.5
        -42.5 122.5
        -42.5 117.5
        -47.5 117.5
        -47.5 112.5
        -57.5 112.5
        -57.5 107.5
        -62.5 107.5
        -62.5 102.5
        -67.5 102.5
        -67.5 97.5
        -72.5 97.5
        -72.5 62.5
        -77.5 62.5
        -77.5 52.5
        -87.5 52.5
        -87.5 47.5
        -92.5 47.5
        -92.5 52.5
        -97.5 52.5
        -97.5 67.5
        -102.5 67.5
        -102.5 77.5
        -107.5 77.5
        -107.5 82.5
        -112.5 82.5
        -112.5 72.5
        -117.5 72.5
        -117.5 62.5
        -122.5 62.5
        -122.5 52.5
        -127.5 52.5
        -127.5 47.5
        -112.5 47.5
        -112.5 42.5
        -102.5 42.5
        -102.5 37.5
        -92.5 37.5
        -92.5 32.5
        -87.5 32.5
        -87.5 22.5
        -82.5 22.5
        -82.5 17.5
        -77.5 17.5
        -77.5 12.5
        -67.5 12.5
        -67.5 7.5
        -62.5 7.5
        -62.5 2.5
        -57.5 2.5
        -57.5 -7.5
        -52.5 -7.5
        -52.5 -12.5
        -47.5 -12.5
        -47.5 -22.5
        -42.5 -22.5
        -42.5 -32.5
        -37.5 -32.5
        -37.5 -62.5
        -42.5 -62.5
        -42.5 -67.5
        -77.5 -67.5
        -77.5 -62.5
        -117.5 -62.5
        -117.5 -57.5
        -122.5 -57.5
        -122.5 -47.5
        -127.5 -47.5
        -127.5 -37.5
        -132.5 -37.5
        -132.5 -17.5
        -137.5 -17.5
        -137.5 2.5
        -142.5 2.5
        -142.5 32.5
        -137.5 32.5
        -137.5 52.5
        -142.5 52.5
        -142.5 57.5
        -147.5 57.5
        -147.5 67.5
        -152.5 67.5
        -152.5 77.5
        -147.5 77.5
        -147.5 87.5
        -152.5 87.5
        -152.5 97.5
        -157.5 97.5
        -157.5 112.5
        -162.5 112.5
        -162.5 122.5
        -167.5 122.5
        -167.5 132.5
        -172.5 132.5
        -172.5 142.5
        -180.0 142.5
===== allowed (blue) region====
region 1
        -180.0 -147.5
        -177.5 -147.5
        -167.5 -147.5
        -167.5 -142.5
        -157.5 -142.5
        -157.5 -137.5
        -147.5 -137.5
        -147.5 -132.5
        -142.5 -132.5
        -142.5 -127.5
        -147.5 -127.5
        -147.5 -97.5
        -152.5 -97.5
        -152.5 -92.5
        -157.5 -92.5
        -157.5 -82.5
        -162.5 -82.5
        -162.5 -52.5
        -157.5 -52.5
        -157.5 -37.5
        -162.5 -37.5
        -162.5 -7.5
        -167.5 -7.5
        -167.5 32.5
        -172.5 32.5
        -172.5 52.5
        -177.5 52.5
        -177.5 77.5
        -180.0 77.5
region 2:
        -42.5 180.0
        -42.5 172.5
        -42.5 172.5
        -37.5 172.5
        -37.5 167.5
        -32.5 167.5
        -32.5 157.5
        -27.5 157.5
        -27.5 147.5
        -22.5 147.5
        -22.5 127.5
        -17.5 127.5
        -17.5 112.5
        -22.5 112.5
        -22.5 107.5
        -27.5 107.5
        -27.5 102.5
        -32.5 102.5
        -32.5 97.5
        -47.5 97.5
        -47.5 92.5
        -52.5 92.5
        -52.5 72.5
        -57.5 72.5
        -57.5 42.5
        -62.5 42.5
        -62.5 27.5
        -57.5 27.5
        -57.5 22.5
        -52.5 22.5
        -52.5 12.5
        -47.5 12.5
        -47.5 7.5
        -42.5 7.5
        -42.5 2.5
        -37.5 2.5
        -37.5 -7.5
        -32.5 -7.5
        -32.5 -12.5
        -27.5 -12.5
        -27.5 -27.5
        -22.5 -27.5
        -22.5 -47.5
        -17.5 -47.5
        -17.5 -67.5
        -22.5 -67.5
        -22.5 -77.5
        -27.5 -77.5
        -27.5 -82.5
        -47.5 -82.5
        -47.5 -87.5
        -77.5 -87.5
        -77.5 -92.5
        -87.5 -92.5
        -87.5 -112.5
        -92.5 -112.5
        -92.5 -122.5
        -97.5 -122.5
        -97.5 -137.5
        -92.5 -137.5
        -92.5 -142.5
        -82.5 -142.5
        -82.5 -147.5
        -72.5 -147.5
        -72.5 -152.5
        -67.5 -152.5
        -67.5 -157.5
        -62.5 -157.5
        -62.5 -162.5
        -57.5 -162.5
        -57.5 -167.5
        -52.5 -167.5
        -52.5 -172.5
        -47.5 -172.5
        -47.5 -177.5
        -42.5 -177.5
        -42.5 -180.0
 region 3:
        82.5 57.5
        87.5 57.5
        87.5 42.5
        92.5 42.5
        92.5 22.5
        97.5 22.5
        97.5 -17.5
        92.5 -17.5
        92.5 -22.5
        87.5 -22.5
        87.5 -27.5
        82.5 -27.5
        82.5 -37.5
        87.5 -37.5
        87.5 -47.5
        92.5 -47.5
        92.5 -57.5
        87.5 -57.5
        87.5 -67.5
        82.5 -67.5
        82.5 -72.5
        77.5 -72.5
        77.5 -77.5
        62.5 -77.5
        62.5 -72.5
        57.5 -72.5
        57.5 -67.5
        52.5 -67.5
        52.5 -37.5
        57.5 -37.5
        57.5 -27.5
        62.5 -27.5
        62.5 -22.5
        57.5 -22.5
        57.5 -12.5
        52.5 -12.5
        52.5 -7.5
        47.5 -7.5
        47.5 -2.5
        42.5 -2.5
        42.5 2.5
        37.5 2.5
        37.5 12.5
        32.5 12.5
        32.5 22.5
        27.5 22.5
        27.5 32.5
        22.5 32.5
        22.5 47.5
        17.5 47.5
        17.5 67.5
        22.5 67.5
        22.5 77.5
        27.5 77.5
        27.5 82.5
        32.5 82.5
        32.5 87.5
        47.5 87.5
        47.5 92.5
        67.5 92.5
        67.5 87.5
        72.5 87.5
        72.5 82.5
        77.5 82.5
        77.5 77.5
        82.5 77.5
        82.5 57.5
 region 4:
        72.5 -102.5
        72.5 -112.5
        77.5 -112.5
        77.5 -157.5
        72.5 -157.5
        72.5 -180.0
        57.5 -180.0
        57.5 -167.5
        52.5 -167.5
        52.5 -162.5
        47.5 -162.5
        47.5 -157.5
        42.5 -157.5
        42.5 -152.5
        37.5 -152.5
        37.5 -142.5
        32.5 -142.5
        32.5 -107.5
        37.5 -107.5
        37.5 -102.5
        42.5 -102.5
        42.5 -97.5
        52.5 -97.5
        52.5 -92.5
        62.5 -92.5
        62.5 -97.5
        67.5 -97.5
        67.5 -102.5
        72.5 -102.5
 region 5:
        77.5 180.0
        77.5 162.5
        82.5 162.5
        82.5 147.5
        72.5 147.5
        72.5 157.5
        67.5 157.5
        67.5 167.5
        62.5 167.5
        62.5 180.0
 region 6:
        162.5 180.0
        162.5 147.5
        167.5 147.5
        167.5 132.5
        172.5 132.5
        172.5 117.5
        177.5 117.5
        177.5 77.5
        180.0 77.5
 region 7:
        162.5 -180.0
        162.5 -177.5
        167.5 -177.5
        167.5 -167.5
        172.5 -167.5
        172.5 -157.5
        177.5 -157.5
        177.5 -147.5
        180.0 -147.5

=========== end of defined values in ramachandran plot ==========

The Gnuplot script is posted at here, in case of missing file in my disc.
The torsion angle file is used as "phipsi.txt" in this script.

==== plot.gnu, use /path/gnuplot plot.gnu to run =======
set terminal png
set output "ramachandran.png"
set noautoscale
set xrange [-180:180]
set xtics -180,30,180 out nomirror
set yrange [-180:180]
set ytics -180,30,180 out nomirror
set tic scale 0.8
set xlabel "phi"
set ylabel "psi"
set arrow from 0, -180 to 0, 180 nohead lw 0.3
set arrow from -180, 0 to 180,0 nohead lw 0.3
set pointsize 0.6
unset key
# LINE COLORS, STYLES
# type 'test' to see the colors and point types available.
# Differs from x11 to postscript
# lt chooses a particular line type: -1=black 1=red 2=grn 3=blue 4=purple 5=aqua 6=brn 7=orange 8=light-brn
# lt must be specified before pt for colored points
#
plot "region1" with l lt 1, "region2" with l lt 1, 
     "region3" with l lt 1, "region-w1" with l lt 3, 
     "region-w2" with l lt 3, "region-w3" with l lt 3, 
     "region-w4" with l lt 3, "region-w5" with l lt 3, 
     "region-w6" with l lt 3, "region-w7" with l lt 3,
     "phipsi.txt" lt -1 pt 5
  • Source: Richardson 2003.[11]

References

  1. ↑ 1.0 1.1 Lovell SC, Davis IW, Arendall WB 3rd, de Bakker PI, Word JM, Prisant MG, Richardson JS, Richardson DC (2003). Structure validation by Calpha geometry: phi,psi and Cbeta deviation. Proteins, 50(3):437-50.
  2. ↑ 2.0 2.1 2.2 Ramachandran: A Java Program For Drawing Ramachandran Plots (accessed: 2006-11-04)
  3. ↑ Kleywegt GJ, Jones TA (1996). Phi/psi-chology: Ramachandran revisited. Structure, 4(12):1395-400.
  4. ↑ Ramachandran revisited (accessed: 2006-11-04)
  5. ↑ 5.0 5.1 Wilmot CM, Thornton JM (1988). Analysis and prediction of the different types of beta-turn in proteins. J Mol Biol, 203:221-32.
  6. ↑ 6.0 6.1 Renugopalakrishnan V, Khaled MA, Rapaka RS, Urry DW (1981). The tetrapeptide, HCO-L-Ala-L-Pro-Gly-Gly-OMe: conformations and solvent effects. Biomolecular Structure, Conformation, Function, and Evolution - Volume 2. Pergamon Press - Oxford.
  7. ↑ Wilmot CM, Thornton JM (1990). "Beta-turns and their distortions: a proposed new nomenclature". Protein Eng, 3:479-93.
  8. ↑ 8.0 8.1 Richardson JS (1981). "The anatomy and taxonomy of protein structure". Adv Protein Chem, 34:167-339. PMID: 7020376.
  9. ↑ Milner-White EJ, Ross BM, Ismail R, Belhadj-Mastefa K, Poet R (1988). "One type of gamma turn, rather than the other, gives rise to chain reversal in proteins". J Mol Biol, 204:777-782.
  10. ↑ Rose GD, Gierasch LM, Smith JA (1985). "Turns in peptides and proteins". Adv Prot Chem, 37:1-109.
  11. ↑ Lovell SC, Davis IW, Arendall WB 3rd, de Bakker PI, Word JM, Prisant MG, Richardson JS, Richardson DC (Feb 2003). "Structure validation by Calpha geometry: phi,psi and Cbeta deviation". Proteins, 50(3):437-50. PMID 12557186.

See also

External links

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