Of course it's always possible for an asymmetric molecule (or part of
a molecule, such as a side-chain) to lie on or near a symmetry axis,
provided it's rotationally disordered with occupancy 0.5 (assuming a
2-fold). In other words half the molecules are randomly distributed
over half of the asymmetric units in one orientation and the other
half are in the other a.u.s in the symmetry-related orientation, so
the copies never clash. The occupancy must be near 0.5 because if it
deviated much from that you would start to see breakdown of the
symmetry of the diffraction pattern (with higher Rmerge etc), and you
would likely conclude that the space group is actually a sub-group of
the original one without the symmetry axis. Obviously it will depend
on the quality of the data, the resolution and the scattering power of
the disorder part whether you are able in practice to detect such a
breakdown of symmetry.
The question here though is whether an atom (say the CG of the ASP) of
the rotationally disordered molecule/part-molecule in such a situation
necessarily lies _on_ a special position. It would be pure
coincidence if it did, for the simple reason that there's absolutely
no reason why it should do so. In other words, because it has
occupancy 0.5 (obviously it must have the same occupancy as the atoms
that it's covalently bonded to, assuming there's no other disorder
present), it must be disordered and so doesn't have to obey the bulk
symmetry. In fact, it would be equally 'happy' slightly displaced
from the special position. There will be no significant minimum in
the internal energy of the system for a disordered atom on a special
position, because the reason it's disordered is that there are no
strong interactions with the surrounding atoms, which would favour one
possible orientation over the other.
This is quite different from the original question posed by Gloria
where (I assume) we have a molecule on a special position where there
is no rotational disorder (it may still have occupancy disorder, i.e.
it may only be present in a fraction of the a.u.s). Here clearly the
occupancy may be > 0.5 for a 2-fold and so no clashes with the
symmetry mate(s) are permitted (assuming of course that the space
group is correct!). In this case the molecule itself must therefore
possess at least the symmetry of the special position, e.g. H2O or SO4
for a 2-fold, as Ralf says. Being ordered (or at least not as
disordered) such a molecule must have strong interactions with its
neighbours, so any shift off the special position would likely result
in an increase in internal energy.
Cheers
-- Ian
On Thu, Dec 9, 2010 at 11:26 AM, <[log in to unmask]> wrote:
> Hi Ralf & Gloria,
>
> It is of course all a matter of definition, but it happens now and again
> that an asymmetric ligand is lying on top of a twofold axis. This is
> usually modeled by fitting the ligand in two orientations at half
> occupancy. In one of the proteins I am working on there is the
> carboxylic acid group of an Asp sitting on a 2-fold axis. I have modeled
> the Asp with 2 alternative conformations: in conformation A, the Asp
> side chain would clash with itself over the 2-fold axis, thus if one
> protein molecule has the Asp in conformation A, the twofold related
> protein molecule must have the Asp in conformation B (or some other
> conformation).
>
> I do not know whether you would call this a Wyckoff position, but side
> chains of proteins do sit on top of crystallographic symmetry axes.
>
> Best,
> Herman
>
> -----Original Message-----
> From: CCP4 bulletin board [mailto:[log in to unmask]] On Behalf Of
> Ralf W. Grosse-Kunstleve
> Sent: Thursday, December 09, 2010 3:47 AM
> To: [log in to unmask]
> Subject: Re: [ccp4bb] Fwd: [ccp4bb] Wyckoff positions and protein atoms
>
> Hi Gloria,
>
> My hobby is space group symmetry.
> My interest phenix development.
>
>> so I can't imagine a protein crystallographer would ever need to
>> apply the modulation function to a protein atom that happened to be
>> on one.
>
> That's true. Protein residues don't have internal symmetry, therefore
> they are not compatible with crystallographic special positions.
> (Wyckoff positions are enumerations of classes of special positions.)
>
> In the PDB molecules with internal symmetry are really rare, except for
> H2O and SO4. But these contribute so little to the total scattering that
> it isn't important to handle them in a special way. So Wyckoff positions
> remain foreign in the macromolecular context.
>
> Ralf
>
>
>
>
> ----- Original Message ----
>> From: Gloria Borgstahl <[log in to unmask]>
>> To: [log in to unmask]
>> Sent: Wed, December 8, 2010 12:16:54 PM
>> Subject: [ccp4bb] Fwd: [ccp4bb] Wyckoff positions and protein atoms
>>
>> I've gotten some interesting responses, that I will summarize for the
>> group later, but I thought I should clarify why I asked.
>>
>> I was worrying about this because I have been working out the steps
>> in how to determine the (3+1)D superspace group for a protein
> crystal.
>> The last step listed in IT vol C chapter 9.8, is to consider any
>> atoms that lie ON a Wyckoff position, and what restrictions this
>> would apply to the modulation function that is refined for each atom.
>>
>> My first reaction, was "Wyckoff positions?" I vaguely remember
>> those, my recollection from my experience was they were really cool,
>> but were usually in the solvent, so I can't imagine a protein
>> crystallographer would ever need to apply the modulation function to a
>
>> protein atom that happened to be on one. But to a crystallographer
>> working on a modulated mineral, it would happen all the time, I'll
> bet.
>> So maybe this was one more thing that just didn't really apply to
>> protein structures and lucky us we don't worry about this last step
>> (just as I never did model that solvent water that was on one, back
>> in the 90s).
>>
>> Then I thought, maybe I'm missing something, or there are special
>> cases out there (and so far I have heard of a disulfide bond on a
>> 2-fold connecting two homodimers).
>>
>> So I polled the collective knowledge of the great ccp4bb group.
>>
>> On Wed, Dec 8, 2010 at 10:57 AM, Gloria Borgstahl
>> <[log in to unmask]>
> wrote:
>> > My fellow crystallographers,
>> > I wanted to take a poll.
>> >
>> > How many of you have ever had a protein atom on a Wyckoff position
>> > (AKA a special position).
>> > What kind of molecules have you found at special positions (it
>> > would have to contain the symmetry of the special position, right?)
>
>> > I'm thinking it is impossible to have a protein atom at a special
>> > position or am I exposing my ignorance yet again...
>> >
>> > my experience is that only once I found an atom in a special
>> > position, it was a strange solvent molecule, that blew my mind for
>> > a while until I learned about special positions in crystallography.
>> >
>> > Looking forward to your responses, Gloria
>> >
>> >
>> > ********************************************************************
>> > ****
>> > Gloria Borgstahl
>> > Eppley Institute for Cancer Research and Allied Diseases
>> > 987696 Nebraska Medical Center
>> > 10732A Lied Transplant Center
>> > Omaha, NE 68198-7696
>> >
>> > http://sbl.unmc.edu
>> > Office (402) 559-8578
>> > FAX (402) 559-3739
>> >
>> > Professor
>> > Hobbies: Protein Crystallography, Cancer, Biochemistry, DNA
>> > Metabolism, Modulated Crystals, Crystal Perfection
>> > Interests: Manga, Led Zepplin, Cold Play, piano, BRAN, RAGBRAI,
>> > golf and lately superspace groups
>> >
>> > ********************************************************************
>> > ****
>> >
>>
>
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