[Biopython] How to apply symmetry matrix on protein chains

[Robert Campbell]

Hello Fred and Bhushan,

One minor correction to what Fred wrote:

On Thu, 2014-11-13 09:59  EST,  Fred Ludlow <fred.ludlow at gmail.com> wrote:

> ps. If you want to understand how it works, or write your own code to do
> it:
> 
> You use the BIOMT records to create a series of 3x3 matrices. e.g. these
> three lines from the PDB file correspond to one transformation:
> 
> REMARK 350   BIOMT1   2  0.500000 -0.809017  0.309017        0.00000
> REMARK 350   BIOMT2   2  0.809017  0.309017 -0.500000        0.00000
> REMARK 350   BIOMT3   2  0.309017  0.500000  0.809017        0.00000
> 
> use these to make a matrix
> 
> >>> import numpy as np
> >>> m = np.array([[ 0.5,      -0.809017,  0.309017],
>               [ 0.809017,  0.30917,  -0.5     ],
>               [ 0.309017,  0.5,       0.809017]])
> 
> Then for each coordinate in your original PDB, e.g. the first one:
> >>> a = np.array([35.887,  31.402,  96.395])
> 
> take the dot product:
> >>> np.dot(m,a)
> array([  22.32644188,   -9.45575058,  104.77588679])

While it doesn't matter in this case because there is no translation in the
BIOMT records of 1HRI, a more complete answer would be:

coord = np.array([35.887,  31.402,  96.395])
rotmat = np.array([[ 0.5,      -0.809017,  0.309017,  0.0],
                   [ 0.809017,  0.30917,  -0.5,       0.0
                   [ 0.309017,  0.5,       0.809017,  0.0]])

rotated_coord = np.dot(rotmat[0:3,0:3],coord) + rotmat[:3,3]

Cheers,
Rob

> On 13 November 2014 06:50, Bhushan <nagbiotech1 at gmail.com> wrote:
> 
> > Hi,
> >
> > I want to apply the symmetry matrix on pdb 1HRI and output the
> > biological assembly (with rotated coordinates). Can anyone suggest me a
> > way to do this using biopython.
> >
> > Thank you for your time. I would appreciate any kind of help.
> >
> >
> > With Regards,
> > Bhushan.
> >
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> > http://mailman.open-bio.org/mailman/listinfo/biopython
> >




-- 
Robert L. Campbell, Ph.D.
Senior Research Associate/Adjunct Assistant Professor
Dept. of Biomedical & Molecular Sciences
Botterell Hall Rm 644
Queen's University, 
Kingston, ON K7L 3N6  Canada
Tel: 613-533-6821
<robert.campbell at queensu.ca>    http://pldserver1.biochem.queensu.ca/~rlc