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Jmol Symmetry View
Introduction
Protein Stoichiometry
The stoichiometry of a protein complex represents the composition of its subunits. For example, the biological assembly of hemoglobin has two alpha and two beta subunits, represented by the stoichiometry formula A2B2. In some cases there is minor heterogeneity among subunits caused by posttranslational modifications, point mutations, or micro-heterogeneity. In the stoichiometry calculation, minor differences among subunits are ignored: if the sequence identity is >= 95% over 90% of the sequence length of two protein chains, they are considered identical. Protein chains with less than 24 residues, nucleic acid chains, and ligands are ignored.
Protein Symmetry
Symmetry refers to the point group symmetry of a protein complex. While a single protein chain with L-amino acids cannot be symmetric (point group C1), protein complexes with quaternary structure can have rotational symmetry belonging to the point groups: cyclic (Cn), dihedral (Dn), tetrahedral (T), octahedral (O), or icosahedral (I). Complexes are considered symmetric if all rotated identical subunits, generated by the symmetry operations of the point group, superpose within <= 5 Å with the original structure. The identity of subunits is based on the same criteria as described for protein stoichiometry.
Pseudostoichiometry and Pseudosymmetry
By default, a 95% sequence identity threshold is used for the stoichiometry and symmetry assignments. In addition, these properties are calculated at 30% sequence identity. If we consider hemoglobin again, at 95% sequence identity threshold the alpha and beta subunits are considered different, which correspond to an A2B2 stoichiometry and a C2 point group. At the 30% sequence identity level, all four chains would be considered homologous (~45% sequence identity) with an A4 pseudostoichiometry and D2 pseudosymmetry. The word pseudo indicates that the stoichiometry and symmetry are approximate.
Split entries (entries divided between multiple coordinate files due to the limitations of the PDB file format) are currently excluded from the protein stoichiometry and protein symmetry features.
Visualizing Protein Symmetry in Jmol
Protein symmetry can be viewed in 3D using Jmol (select the "View in 3D" link on an entry's Structure Summary page). Protein symmetry is calculated for all entries containing at least one protein chain, including asymmetric units and all biological assemblies (except for entries split among several PDB files due to their size). The Jmol page for each asymmetric unit or biological assembly is accessible from the "View in 3D" link on every structure summary page.
To facilitate the exploration of symmetry, several options are available:
Default Orientation
Protein complexes are aligned along the highest-order symmetry axis or along the principal axes on inertia for asymmetric cases. Several default orientations of the structure can be toggled using the < and > buttons. The default orientations are canonical views: sides and back, and along unique n-fold symmetry axes.
View PDB ID 3EAM in JmolSymmetry polyhedra and axes
A polyhedron and symmetry axes can be displayed to facilitate symmetry analysis of symmetry. A complex is enclosed in a polyhedron that matches its symmetry. All symmetry axes and their icons representing the fold (ellipsis for 2-fold, triangle for 3-fold axis, or in general a polygon for n-fold axis) can be displayed. For asymmetric cases, the 3 axes of inertia are displayed. Polyhedron and Axes can be toggled on/off using the check boxes in the right panel.
View PDB ID 1AEW in JmolSubunit colors
Structures can be colored by symmetry (see table below), sequence (subunits with >= 95% sequence identity shown in the same color), or by subunit. Two examples of structures colored by symmetry are shown below. 
Example 1
For Cn symmetry (see example on left), the color scheme start at the 12 o'clock position, and the color gradient (light to dark) increases in a clockwise direction. The polyhedron, a pentagonal prism is displayed in a color complementary to the symmetry color scheme. The principal rotation axis is rendered in red with a pentagon representing the 5-fold rotation.
View PDB ID 3EAM in Jmol
Example 2
In all cubic systems (T, O, I), different layers of the subunit are colored along a gradient (light to dark) from the plus and minus z-axis towards the origin (see example on left). The 4-fold axes are rendered in red, the 3-fold axes in green, and the 2-fold axes in blue. Using the toggle option underneath the Jmol applet, 3 views along these 3 different axes are available.
View PDB ID 1SHS in JmolSetting the sequence identity threshold
The display of symmetry depends on the sequence identity threshold. Either a 95% (default, far left) or 30% (left) sequence identity thresholds can be selected. At the lower identity level, some complexes may have pseudosymmetry, which is demonstrated with the hemoglobin example in the images to the left.
View PDB ID 4HHB in Jmol
Symmetry Color Schemes
| Symmetry | Color Scheme | Example | Image | Polyhedron | Axes |
|
Cyclic C1 (no symmetry) |
grays |
PDB: 4AJY Stoichiometry: ABC Point Group: C1 |
|
rectangular prism gray |
3 axes of inertia in gray |
|
Cyclic Cn |
yellow-green-blue radial gradient clockwise around symmetry axis |
PDB: 4ACV Stoichiometry: A6 Point group: C6 |
|
hexagonal prism orange |
6-fold red |
|
Dihedral Dn |
yellow-orange- red gradient along z-axis towards origin |
PDB: 1YA7 Stoichiometry:A14B14C14 Point group: D7 |
|
heptagonal prism blue |
7-fold red 2-fold blue |
|
Tetrahedral T |
green gradient (light - dark) along z-axis towards origin |
PDB: 1MOG Stoichiometry: A12 Point group: T |
|
tetrahedron purple |
3-fold green 2-fold blue |
|
Octahedral O |
blue gradient (light - dark) along z-axis towards origin |
PDB: 1SHS Stoichiometry:A24 Point group O |
|
octahedron orange |
4-fold red 3-fold green 2-fold blue |
|
Icosahedral I |
blue-purple gradient along z-axis towards origin |
PDB: 4FTS Stoichiometry:A180 |
|
icosahedron green |
5-fold red 3-fold green 2-fold blue |