Given the PDB or mmCIF file of a protein, how might one design an algorithm to find which point group symmetry class it belongs to (cyclic C_n, dihedral D_n, or neither) without requiring manual inspection?
More than finding out tools that already do this, I would like to know if there is a simple mathematical approach for the same.
One idea I had for detecting cyclic symmetry was to calculate the centroid of each subunit in a homomer (for instance). If there indeed is some cyclic symmetry, the axis must pass through the global centroid, and it must be normal to the plane formed by the individual subunit centroids. To test if this axis is indeed valid, one can rotate the entire protein about the axis by 2pi / n, and check that the atomic coordinates align closely with those of the original (using RMSD for example).
But I'm having trouble thinking about dihedral symmetry, specifically for simple homomers. Any help on this would be appreciated.
