Hi,
If you go to
http://cci.lbl.gov/cctbx/explore_symmetry.html
fill out any space group (F432), and search for:
Additional generators of Euclidean normalizer
to get
Number of structure-seminvariant vectors and moduli: 1
Vector Modulus
(1, 0, 0) 2
The seminvariants for F432 are thus
(1/2, 0, 0)
so the only unique origin shift to consider here is (1/2,0,0).
The 1/4 solution do not arise in F432 as can be seen in
http://scripts.iucr.org/cgi-bin/paper?a10657 (table 4) as well.
Giacovazzo actually lists 1/2 1/2 1/2, which is symmetry equivalent to
1/2 0 0 (F centering).
In the cctbx, these seminvariants are derived from first principles
and do work as well when you have things in weird settings. One nice
application of doing this from first principles over using lookup
tables, is (for instance) finding "pseudo" origin shifts in the
presence translational NCS.
For instance the origin shifts in P21:
------------------
Number of structure-seminvariant vectors and moduli: 3
Vector Modulus
(1, 0, 0) 2
(0, 1, 0) 0 <- continuous shift along y
(0, 0, 1) 2
Inversion through a centre at: 0,0,0
------------------
and in P21 with added (pseudo) (x+1/2,y,z), one gets
------------------
Number of structure-seminvariant vectors and moduli: 3
Vector Modulus
(1, 0, 0) 4
(0, 1, 0) 0
(0, 0, 1) 2
Inversion through a centre at: 0,0,0
------------------
This indicates that you have an additional origin shift of (1/4,0,0)
when you have (x+1/2,y,z) as part of the symmetry. If (x+1/2,y,z) is a
'pseudo' operator, then the origin shift of (1/4,0,0) will be pseudo
as well. This can lead to interesting molecular replacement problems
(Andrey Lebedev has done some nice work there).
Cheers,
Peter
2010/1/27 James Holton <[log in to unmask]>:
> Francois Berenger wrote:
>>
>> It correspond to what is found at the end of James Holton's
>> origins.com script
>> http://bl831.als.lbl.gov/~jamesh/pickup/origins.com
>> so I guess it should be correct.
>
> Uhhh...
>>
>> He also says how he found them:
>> <origins.com snippet>
>> # TABLE OF ALLOWED ORIGIN SHIFTS
>> These origin shifts were determined emprirically using 100 randomly-placed
>> atoms
>> that were shifted around with pdbset and checked with SFALL for identical
>> amplitudes to the 0 0 0 origin. They should be correct for the CCP4
>> convention
>> of symmetry. (I.E. R3 and R32 have hexagonal indexing)
>> </origins.com snippet>
>
> Okay, I just went back to my notes on this. I should admit that in my
> completely brain-dead allowed-origin-shift search described above I
> originally found no "allowed" shifts for F432 (not sure why, but maybe
> because it was last on my list). Years later, I think it was Peter Zwart who
> pointed out to me that I was missing a few of what ought to be allowed
> origins. As I recall, at least one of them passed my pdbset/sfall test, so
> I just assumed I must have done something wrong and added everything in the
> CCP4 document and ITC Vol B to the list. For purposes of the origins.com
> script, I decided to err on the side of having it try things that may or may
> not work. If it finds a match, then great! Right?
>
> Perhaps this was not wise of me. I just tried shifting the 2fka PDB file by
> "SHIFT FRAC 0.25 0.25 0.25" with pdbset and comparing the resulting Fs from
> sfall to those of the un-shifted PDB. They are ~30% different. It could be
> that this is a bug in sfall or pdbset (doubtful), but I would say that
> pragmatically, this is not an "allowed origin shift" for F432. However,
> 0,0,0.5 and 0,0.5,0.5 and all the other half-cell combinations do work!
> Guess I missed those! I have now updated my origins.com script. It
> appears that the allowed origin shifts for F432 and F23 are not the same, as
> I had previously thought.
>
>>
>>> plus of course the symmetry-equivalent origins generated from these 4 by
>>> the space-group centring (F) translations:
>>>
>>> 0.0000 0.5000 0.5000
>>> 0.5000 0.0000 0.5000
>>> 0.5000 0.5000 0.0000
>>
>> I can see these in syminfo.lib.
>>
>> However, from what you say, I understand that only 2x3 possible
>> origins with each coordinate being 0 or .5 should be accepted by
>> reforigin.
>> But in my test it accepted all 8 possible combinations of 0 and .5
>> that I artificially introduced in my translated test PDBs:
>>
>> m@myPS:2fka# grep Frac run.log | sort | uniq
>> Fractional origin shift: 0.0000 0.0000 0.0000
>> Fractional origin shift: 0.0000 0.0000 0.5000
>> Fractional origin shift: 0.0000 0.5000 0.0000
>> Fractional origin shift: 0.0000 0.5000 0.5000
>> Fractional origin shift: 0.5000 0.0000 0.0000
>> Fractional origin shift: 0.5000 0.0000 0.5000
>> Fractional origin shift: 0.5000 0.5000 0.0000
>> Fractional origin shift: 0.5000 0.5000 0.5000
>>
>> Should I be worried?
>
> At this point, I would say no. Reforigin seems to be doing it right.
>
> I think some of the confusion might be arising because an "alternate origin"
> and a fractional coordinate shift that gives you the same structure factor
> amplitudes may or may not be the same thing. Some shifts change the phase,
> but not the amplitude so whether or not they are "alternate" depends on what
> you are trying to do.
> -James Holton
> MAD Scientist
>
>>
>> Thanks,
>> Francois.
>>
>>> So there will be 12 in all, which I think include the ones you
>>> mentioned.
>>>
>>> If you're going by
>>> http://www.ccp4.ac.uk/dist/html/alternate_origins.html then you should
>>> be aware of a very recent BB discussion in which it was pointed out that
>>> the entries for F222, F23, F432 and possibly others are incomplete.
>>>
>>> Eleanor has given me the task of checking & correcting this particular
>>> documentation, until then don't trust it!
>>>
>>> Of course you shouldn't trust reforigin either, just as you shouldn't
>>> trust any program until you have verified that the results are sensible,
>>> but I think in this particular the fault doesn't lie with reforigin.
>>>
>>> Cheers
>>>
>>> -- Ian
>>>
>>>> -----Original Message-----
>>>> From: [log in to unmask] [mailto:[log in to unmask]]
>>>
>>> On
>>>>
>>>> Behalf Of Francois Berenger
>>>> Sent: 27 January 2010 06:50
>>>> To: [log in to unmask]
>>>> Subject: reforigin on 2FKA
>>>>
>>>> Hello,
>>>>
>>>> I am playing with ccp4's reforigin to verify some MR solutions.
>>>>
>>>> If I translate a copy of the pdb.org's PDB 2FKA (from spacegroup F432)
>>>> by +/-0.5 fractional in any unit cell direction, then reforigin will
>>>> find back this translation and consider it as valid for this
>>>
>>> spacegroup.
>>>>
>>>> But for this spacegroup I should find only (0,0,0) or (1/2,1/2,1/2)
>>>> as possible alternate origins.
>>>>
>>>> Does this mean that I can't trust reforigin and that I must filter
>>>> out its results to retain only the valid ones?
>>>>
>>>> Thanks,
>>>> Francois.
>>>
>>>
>>>
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--
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P.H. Zwart
Beamline Scientist
Berkeley Center for Structural Biology
Lawrence Berkeley National Laboratories
1 Cyclotron Road, Berkeley, CA-94703, USA
Cell: 510 289 9246
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