Dihedral/Dihedral angles in proteins

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The model displayed on the right is a tripeptide (Trp<sub>34</sub>&ndash;Glu<sub>35</sub>&ndash;Ser<sub>36</sub> within the protein lysozyme).
The model displayed on the right is a tripeptide (Trp<sub>34</sub>&ndash;Glu<sub>35</sub>&ndash;Ser<sub>36</sub> within the protein lysozyme).
This page illustrates the meaning of '''phi (&#x03D5;)''' and '''psi (&#x03C8;)''' angles, both around the alpha carbon of the central residue (Glu<sub>35</sub>). Both are '''''dihedral angles''''', meaning an angle formed between two planes (as compared to regular angles, formed between two lines or bonds).
This page illustrates the meaning of '''phi (&#x03D5;)''' and '''psi (&#x03C8;)''' angles, both around the alpha carbon of the central residue (Glu<sub>35</sub>). Both are '''''dihedral angles''''', meaning an angle formed between two planes (as compared to regular angles, formed between two lines or bonds).
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They are also called ''torsion angles'', meaning the torsion or rotation around a bond.
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They are also called '''''torsion angles''''', meaning the torsion or rotation around a bond.
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<!--
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Note that each alpha carbon (residue ''i'') belongs to two peptide planes (with residues ''i&minus;1'' and ''i+1'' respectively).
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-->
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phi (&#x03D5;) is defined by these two planes:
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'''phi (&#x03D5;)''' is the angle between these two planes:
* plane defined by C<sub>i&minus;1</sub>, N<sub>i</sub> and C<sup>&alpha;</sup><sub>i</sub><br>displayed as <span style="background-color:thistle; padding:0 1.5ex; margin-right:0.5ex; font-size:0.7em;"></span><span style="font-size:0.7em; color:#555;">(1)</span>
* plane defined by C<sub>i&minus;1</sub>, N<sub>i</sub> and C<sup>&alpha;</sup><sub>i</sub><br>displayed as <span style="background-color:thistle; padding:0 1.5ex; margin-right:0.5ex; font-size:0.7em;"></span><span style="font-size:0.7em; color:#555;">(1)</span>
* plane defined by N<sub>i</sub>, C<sup>&alpha;</sup><sub>i</sub> and C<sub>i</sub><br>displayed as <span style="background-color:plum; padding:0 1.5ex; margin-right:0.5ex; font-size:0.7em;"></span><span style="font-size:0.7em; color:#555;">(2)</span>
* plane defined by N<sub>i</sub>, C<sup>&alpha;</sup><sub>i</sub> and C<sub>i</sub><br>displayed as <span style="background-color:plum; padding:0 1.5ex; margin-right:0.5ex; font-size:0.7em;"></span><span style="font-size:0.7em; color:#555;">(2)</span>
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Therefore ϕ means rotation around the N-C<sup>&alpha;</sup> bond.
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Therefore ϕ means rotation around the N—C<sup>&alpha;</sup> bond.
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psi (&#x03C8;) is defined by these two planes:
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'''psi (&#x03C8;)''' is the angle between these two planes:
* plane defined by N<sub>i</sub>, C<sup>&alpha;</sup><sub>i</sub> and C<sub>i</sub><br>displayed as <span style="background-color:moccasin; padding:0 1.5ex; margin-right:0.5ex; font-size:0.7em;"></span><span style="font-size:0.7em; color:#555;">(3)</span>
* plane defined by N<sub>i</sub>, C<sup>&alpha;</sup><sub>i</sub> and C<sub>i</sub><br>displayed as <span style="background-color:moccasin; padding:0 1.5ex; margin-right:0.5ex; font-size:0.7em;"></span><span style="font-size:0.7em; color:#555;">(3)</span>
* plane defined by C<sup>&alpha;</sup><sub>i</sub>, C<sub>i</sub> and N<sub>i+1</sub><br>displayed as <span style="background-color:sandybrown; padding:0 1.5ex; margin-right:0.5ex; font-size:0.7em;"></span><span style="font-size:0.7em; color:#555;">(4)</span>
* plane defined by C<sup>&alpha;</sup><sub>i</sub>, C<sub>i</sub> and N<sub>i+1</sub><br>displayed as <span style="background-color:sandybrown; padding:0 1.5ex; margin-right:0.5ex; font-size:0.7em;"></span><span style="font-size:0.7em; color:#555;">(4)</span>
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Therefore ψ means rotation around the C<sup>&alpha;</sup>-C bond.
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Therefore ψ means rotation around the C<sup>&alpha;</sup>—C bond.
:Note that planes 2 and 3 coincide.
:Note that planes 2 and 3 coincide.
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:In all these, "C" means the carboxylic carbon, forming the amide or peptide bond
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:In all these, "C" means the carboxylic carbon, forming the amide or peptide bond with the N. Peptide bonds are displayed in black.
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You can run animations that continuously rotate the model changing one of the angles:
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You can run '''animations''' that continuously rotate the model changing one of the angles.
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<!--, or use the slider or controls to manually progress through different values of the angles.-->
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First, select one of the angles:
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<big>
<jmol>
<jmol>
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<jmolButton>
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<jmolRadioGroup>
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<text>Prepare ϕ</text>
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<item>
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<script>zap; set echo middle center; echo please wait...; refresh; script /wiki/images/c/ce/Phi-rot_uni.spt; e_legend; select all;labels off;</script>
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<script>zap; set echo middle center; echo please wait...; refresh; script /wiki/images/c/ce/Phi-rot_uni.spt; set measurements 0.25;</script>
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</jmolButton>
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<text>ϕ</text>
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</item>
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<item>
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<script>zap; set echo middle center; echo please wait...; refresh; script /wiki/images/2/22/Psi-rot_uni.spt; set measurements 0.25; e_legend; select all;labels off;</script>
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<text>ψ</text>
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</item>
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</jmolRadioGroup>
</jmol>
</jmol>
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animation, and then:
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</big>
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<jmol>
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<jmolButton>
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<text>play/pause</text>
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<script>if(_animating) {frame pause} else {frame play}</script>
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</jmolButton>
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</jmol>
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<jmol>
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After the model has loaded,
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<jmolButton>
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<text>Prepare ψ</text>
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<script>zap; set echo middle center; echo please wait...; refresh; script /wiki/images/2/22/Psi-rot_uni.spt; e_legend; select all;labels off;</script>
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</jmolButton>
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</jmol>
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animation, and then:
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<jmol>
<jmol>
<jmolButton>
<jmolButton>
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</jmol>
</jmol>
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<span style="color:#F000F0;">'''Magenta cylinders'''</span> are displayed where neighbour atoms collide (hence there is an unfavourable conformation for those particular ϕ, ψ values).
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'''Clashes''': <span style="color:#F000F0;">'''magenta cylinders'''</span> are displayed where neighbour atoms collide (hence there is an unfavourable conformation for those particular ϕ, ψ values).
</div>
</div>
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<uploadedFileContents>1iy4_34-36.pdb</uploadedFileContents>
<uploadedFileContents>1iy4_34-36.pdb</uploadedFileContents>
<pspeed>8</pspeed>
<pspeed>8</pspeed>
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<script>script /wiki/images/0/0c/Phi-Psi_uni.spt; function e_legend() { draw id "d_N" fixed diameter 2 [90 95%] color @{{_N}.color};set echo id "e_N" [91 94%];echo N;color echo @{{_N}.color}; draw id "d_CA" fixed diameter 2 [90 90%] color [x70AB70];set echo id "e_CA" [91 89%];echo "C\u03B1";color echo [x70AB70]; draw id "d_CO" fixed diameter 2 [90 85%] color [xBF9090];set echo id "e_CO" [91 84%];echo "C=O";color echo [xBF9090]; draw id "d_O" fixed diameter 2 [90 80%] color @{{_O}.color};set echo id "e_O" [91 79%];echo "O";color echo @{{_O}.color}; draw id "d_C" fixed diameter 2 [90 75%] color @{{35.CB}.color};set echo id "e_C" [91 74%];echo "C";color echo @{{35.CB}.color}; } e_legend; select all;labels off;</script>
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<script>script /wiki/images/0/0c/Phi-Psi_uni.spt; function e_legend() { draw id "d_N" fixed diameter 2 [88 95%] color @{{_N}.color};set echo id "e_N" [90 94%];echo N;color echo @{{_N}.color}; draw id "d_CA" fixed diameter 2 [88 90%] color [x70AB70];set echo id "e_CA" [90 89%];echo "C\u03B1";color echo [x70AB70]; draw id "d_CO" fixed diameter 2 [88 85%] color [xBF9090];set echo id "e_CO" [90 84%];echo "C=O";color echo [xBF9090]; draw id "d_O" fixed diameter 2 [88 80%] color @{{_O}.color};set echo id "e_O" [90 79%];echo "O";color echo @{{_O}.color}; draw id "d_C" fixed diameter 2 [88 75%] color @{{35.CB}.color};set echo id "e_C" [90 74%];echo "C";color echo @{{35.CB}.color}; } e_legend; select all;labels off;</script>
</jmolApplet>
</jmolApplet>
</jmol>
</jmol>

Current revision

The model displayed on the right is a tripeptide (Trp34–Glu35–Ser36 within the protein lysozyme). This page illustrates the meaning of phi (ϕ) and psi (ψ) angles, both around the alpha carbon of the central residue (Glu35). Both are dihedral angles, meaning an angle formed between two planes (as compared to regular angles, formed between two lines or bonds). They are also called torsion angles, meaning the torsion or rotation around a bond.


phi (ϕ) is the angle between these two planes:

  • plane defined by Ci−1, Ni and Cαi
    displayed as (1)
  • plane defined by Ni, Cαi and Ci
    displayed as (2)

Therefore ϕ means rotation around the N—Cα bond.


psi (ψ) is the angle between these two planes:

  • plane defined by Ni, Cαi and Ci
    displayed as (3)
  • plane defined by Cαi, Ci and Ni+1
    displayed as (4)

Therefore ψ means rotation around the Cα—C bond.

Note that planes 2 and 3 coincide.
In all these, "C" means the carboxylic carbon, forming the amide or peptide bond with the N. Peptide bonds are displayed in black.

You can run animations that continuously rotate the model changing one of the angles.

First, select one of the angles:

After the model has loaded,

Clashes: magenta cylinders are displayed where neighbour atoms collide (hence there is an unfavourable conformation for those particular ϕ, ψ values).

Drag the structure with the mouse to rotate

Proteopedia Page Contributors and Editors (what is this?)

Angel Herraez

Retrieved from "http://52.214.119.220/wiki/index.php/Dihedral/Dihedral_angles_in_proteins"
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