Well practically speaking the opposite superimpositions are not
performed in the same fashion. Lets take 1ONE and 2ONE as an example,
2 different conformations of the same molecule. Since the aa
composition is identical (at least from what I've seen the chains have
the same length), I measured the distances between Ca atoms of 1ONE
and 2ONE after "align 1ONE and chain A, 2ONE and chain A", and the
respective distances after "align 2ONE and chain A, 1ONE and chain A".
The RMSD is 0.230642045187 which implies that the 2 chains are not in
relative positions after 1ONEx2ONE and 2ONEx1ONE. Here's the function
I 've written to do that:
# a function to measure Ca distances of oposite pairs of superimpossed
chains (the proteins must have the same aa composition)
def check_for_symmetry(tstruct, qstruct):
# align the pair
cmd.fetch(tstruct)
cmd.extract(pdb2entry[tstruct]+"1", tstruct + " and chain "+
pdb2entry[tstruct][-1:] + " and not hetatm")
cmd.fetch(qstruct)
cmd.extract(pdb2entry[qstruct]+"1", qstruct +" and chain "+
pdb2entry[qstruct][-1:] + " and not hetatm")
print "Aligning "+pdb2entry[tstruct]+"1"+" with "+pdb2entry[qstruct]+"1"
cmd.align(pdb2entry[tstruct]+"1", pdb2entry[qstruct]+"1")
#cmd.do("cealign "+pdb2entry[qstruct]+"1, "+pdb2entry[tstruct]+"1")
# align the symmetric pair
cmd.fetch(tstruct)
cmd.extract(pdb2entry[tstruct]+"2", tstruct + " and chain "+
pdb2entry[tstruct][-1:] + " and not hetatm")
cmd.fetch(qstruct)
cmd.extract(pdb2entry[qstruct]+"2", qstruct +" and chain "+
pdb2entry[qstruct][-1:] + " and not hetatm")
print "Aligning "+pdb2entry[qstruct]+"1"+" with "+pdb2entry[tstruct]+"1"
cmd.align(pdb2entry[qstruct]+"2", pdb2entry[tstruct]+"2")
#cmd.do("cealign "+pdb2entry[qstruct]+"2, "+pdb2entry[tstruct]+"2")
# measure distances
pymol.stored.protein_dict = {}
cmd.iterate(pdb2entry[tstruct]+"1", "stored.protein_dict[(chain,resi)]=1")
Residues = pymol.stored.protein_dict.keys()
Residues.sort()
RMSD = 0
for res in Residues:
chain = res[0]
resi = res[1]
dist1 = cmd.distance('tmp',pdb2entry[tstruct]+"1 and chain
"+chain+" and resi "+resi+" and name ca",pdb2entry[qstruct]+"1 and
chain "+chain+" and resi "+resi+" and name ca")
dist2 = cmd.distance('tmp',pdb2entry[tstruct]+"2 and chain
"+chain+" and resi "+resi+" and name ca",pdb2entry[qstruct]+"2 and
chain "+chain+" and resi "+resi+" and name ca")
print "The difference in distance betweem residue IDs ",
resi," is : ",dist1, "-",dist2," = ",dist1-dist2
RMSD += (dist1-dist2)**2
RMSD = sqrt(RMSD/len(Residues))
print "RMSD of distances between identical residues in 1ONE x
2ONE and this in 2ONE x 1ONE: ", RMSD
check_for_symmetry("1ONE", "2ONE")
PS: Jason, I suspect the same happens with CEalign although I couldn't
manage to run it for technical reasons, but by looking at the
transformation matrices produced by the stand-alone version, the
translation vectors are not opposite.
> Hi Thomas,
>
> Say, the first system is x and the second y, where y=R(x+s) is the
> first transformation. Then the reverse transformation follows as
>
> y = R(x + s)
> y = Rx + Rs
> Rx = y - Rs
> x = t(R)(y-Rs)
>
> Note that that is also equal to: x = t(R)y - s
>
> Hope it helps,
>
> Tsjerk
>
> On Mon, Nov 9, 2009 at 1:09 AM, Thomas Evangelidis
> <[email protected]> wrote:
>> Dear pymol users,
>>
>> I noticed something strange when superimposing 2 opposite pairs of
>> chains. E.g.
>>
>> DEBUG: template 1BQG_A query 2MUC_A
>> Query Transformation:
>> X2 = +0.86747*(X1+2.29751) + -0.49574*(Y1+60.99794) +
>> -0.04181*(Z1+64.71239)
>> Y2 = -0.49701*(X1+2.29751) + -0.85983*(Y1+60.99794) +
>> -0.11697*(Z1+64.71239)
>> Z2 = +0.02204*(X1+2.29751) + +0.12225*(Y1+60.99794) +
>> -0.99226*(Z1+64.71239)
>>
>>
>> DEBUG: template 2MUC_A query 1BQG_A
>> Query Transformation:
>> X2 = +0.86747*(X1+30.95128) + -0.49701*(Y1+61.15895) +
>> +0.02204*(Z1+56.70381)
>> Y2 = -0.49574*(X1+30.95128) + -0.85983*(Y1+61.15895) +
>> +0.12225*(Z1+56.70381)
>> Z2 = -0.04181*(X1+30.95128) + -0.11697*(Y1+61.15895) +
>> -0.99226*(Z1+56.70381)
>>
>> Although looking at the rotation matrices one is the transpose of the
>> other, the translation vectors are not opposite. Can someone explain
>> that?
>>
>>
>>
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>
>
>
> --
> Tsjerk A. Wassenaar, Ph.D.
> Junior UD (post-doc)
> Biomolecular NMR, Bijvoet Center
> Utrecht University
> Padualaan 8
> 3584 CH Utrecht
> The Netherlands
> P: +31-30-2539931
> F: +31-30-2537623
>
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