Dear Ian,
Of course there is no dicontinuity, but you create one the moment you decide that certain symmetry operators no longer apply to certain atoms. Confusion arises e.g. when you download a pdb file of fairly high resolution and find a water molecule with an occupancy of e.g. 0.45 at 0.02 Å from a symmetry axis. Is it a special water suffering from some rounding errors with a total occupancy of 0.45, or a rotationally disordered water (perhaps refined by an overzealous crystallographer) with a combined occupancy of 0.90?
This in my eyes unneccessary distinction between special and non-special positions does create confusion and unnecessarily complicates the programming of programs working with coordinates files. If certain refinement program have difficulties with atoms close to symmetry axes, one could always add the approprioate constraints of restraints.
Cheers,
Herman
-----Original Message-----
From: CCP4 bulletin board [mailto:[log in to unmask]] On Behalf Of Ian Tickle
Sent: Thursday, December 16, 2010 1:31 PM
To: [log in to unmask]
Subject: Re: [ccp4bb] Fwd: [ccp4bb] Wyckoff positions and protein atoms
> You still have an arbitrary threshold: at high resolution you see two disordered atoms off-axis and at low resolution you see one ordered atom on-axis. However, somewhere in between you or the program has to decide whether you still see two atoms or if the data (resolution) does not warrant such a statement and you switch to the one-atom model.
Switching between interpretations happens all the time as higher resolution data is obtained! Let's say at low resolution you see density apparently for one copy of a side-chain (i.e. the density is not of sufficient resolution to warrant interpreting it as disordered two half side-chains) and you fit that. To keep it simple I'm assuming it's on a general, not a special position. Then you collect high-resolution data and now you see that the same side-chain is disordered. Rephrasing your statement: "somewhere in between you or the program has to decide whether you still see one (ordered, with
occupancy=1) side-chain or if the data (resolution) warrants such a statement and you switch to the two side-chain (disordered, now with sum occupancy=1) model".
> As George Sheldrick confirmed, there is a discontinuous transition between the two, which does not correspond to the physical reality. There is no "quantum transition" or something when the atom get closer than a certain limit to a crystallographic symmetry element. The atom does not care, its position is just determined by the local force fields and if those force fields have two local minima close together, the atom will be disordered.
I'm sorry I don't see this discontinuity that you are referring to at all (I think you have forgotten to include the symmetry copy), and I'm certainly not claiming there is any "quantum transition". Let's start with a disordered (1/2 occupancy) atom off a 2-fold axis and see what happens to the electron density as it approaches and finally sits on the 2-fold. Here are the electron densities (this would obviously look at lot better graphed - my apologies!):
1 6 10 6 1 * 1 6 10 6 1
Now move the atom closer in steps to the axis so it overlaps more and more with its symmetry copy:
*
1 6 10 6 2 6 10 6 1
1 6 10 7 7 10 6 1
1 6 11 12 11 6 1
1 7 16 16 7 1
2 12 20 12 2
*
On the final step the fully overlapped atom has twice the occupancy (i.e. 1 instead of 1/2) as the original as evidenced by a peak height of 20 units, compared with 10. In which step did the discontinuity occur? Clearly we could make the steps as small as we like, and you would see a smooth transition from 2 1/2 atoms to 1 whole one.
> The decision to switch from a model where the atom is added once with full occupancy to the fourier transform calculation, or whether the atom is added twice with half occupancy is an arbitrary decision, made by the programmer or the user of the program.
I completely agree, both ways of doing it work equally well and it's all down to convention. As I pointed out to Dale, the way I'm describing does work in practice, as evidenced by the fact that CRYSTALS which does it the way I describe, has been doing it this way for the last 40 years. So I can't accept that it can't work in practice when plainly it does!
This issue here is purely one of divergence of agreed convention (CIF, mmCIF & PDB) and practice.
Cheers
-- Ian
