I am working with virus coat protein PDB ID: 1HRI which has 60 symmetry matrices. I have calculated the theta (angle of rotation) and rotation per axis also for every matrix, Now from these theta values, how can I identify the symmetry fold (like 2 fold (180o), 3 fold (120o), 6 fold (60o) etc.,).
I am attaching the python code (math is taken from a webpage and was implemented in the code)
http://www.euclideanspace.com/maths/geometry/rotations/conversions/matrixToAngle/
To run the code issue the below command in terminal:
python rotate.py
This will generate a pdb file with biological assembly (though not necessary for the current query).
Awaiting your reply,
Thanks to everyone for their time.
With Regards,
Bhushan
The problem is that the symmetry operations used to generate the virus capsid are mostly non-crystallographic symmetries, e.g. rotation around five-fold axes, therefore decomposing the symmetry matrix into angles of rotation around the crystal axes is not helpful in identifying the non-crystallographic symmetries. See http://viperdb.scripps.edu/mat.php?tnum=60 for an explanation of which symmetry matrix corresponds to the rotational components of the transformation between any two faces of the icosahedron.
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