Dear all,
just to add that Clemens Vonrhein already a few years ago has implemented a procedure
similar to the one Simon describes, to automatically fill the cavities in the macromolecule
before computing the mask for the solvent, thus avoiding placing solvent where
the core of the protein is, in the refinement suite autoBUSTER.
It works!
Incidentally, plotting the correlation coefficients between the Fobs and the F
computed from the model alone (i.e. without babinet solvent correction) and the
one bewteen Fobs and the full Fcalc (also a plot acessible during autoBUSTER
refinement), one can easily see differences all the way up to 5 A.
Regards
Pietro
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From: CCP4 bulletin board [[log in to unmask]] On Behalf Of Simon Phillips [[log in to unmask]]
Sent: 25 October 2010 09:09
To: [log in to unmask]
Subject: [ccp4bb] FW: [ccp4bb] Babinet solvent correction [WAS: R-free flag problem]
Dear Tim,
Interesting discussion, and I agree with your last description of the issues. When I started playing with this for oxymyoglobin [J. Mol. Biol. 142, 531-544 (1980)]
it seemed immediately apparent (i.e. by thinking about it before starting to write programs) that the simple Babinet approach was deficient since the solvent was not just the inverse of the protein. This is Tim's point about not using Fc in the Babinet method because protein density is not flat (but you could use a flat protein model Fm). As pointed out in this discussion, there is not much difference between the two at 20A resolution anyway, but what did become apparent when I started doing actual calculations was that the solvent effect was noticeable even at moderate resolutions. It seemed to me then that the obvious was to go was a flat solvent to generate Fs. The issues then were where to put the protein-solvent boundary, and how sharp to make it (i.e. a B factor).
I also noticed that when the mask was made, small cavities in the protein would generate bits of "solvent" in the interior of the protein that should not be there (another issue alluded to in the discussion). In those days I was looking at maps/masks plotted on paper rather than graphics, and I solved the cavity problem manually by adding atoms in the cavities in the pdb file I used to make the mask until I couldn't see any more cavities left in a plot. This is not, of course, an automatic procedure, and that would need a bit of thought. The determination of the border width between protein and solvent, and the B factor, were just optimised by trial and error, running several values, plotting R factors and fitting a function to them (parabola I think) to help find a minimum. Again the issue for automating this requires finding suitable parameters with derivatives.
Having done all this in a simple-minded way, I was very impressed by the effect on the refinement, and on of the figures in the JMB paper shows how dramatic it was and how far up the resolution range the effect was felt. At this stage I should have programmed it properly, but the oxymyglobin structure was done, I had to move jobs and projects and good intentions fell by the wayside (mea culpa). Luckily more public spirited people picked up some of the ideas and improved them, but the protein cavity issue is still there it seems.
Obviously I would like to add my vote for a proper flat (or nearly?) solvent mask model as being the right apporach.
Simon
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-----Original Message-----
From: CCP4 bulletin board [mailto:[log in to unmask]] On Behalf Of Tim Fenn
Sent: 23 October 2010 21:14
To: [log in to unmask]
Subject: Re: [ccp4bb] Babinet solvent correction [WAS: R-free flag problem]
On Sat, 23 Oct 2010 10:05:15 -0700
Pavel Afonine <[log in to unmask]> wrote:
> Hi Tim,
>
> ...but I hope this answers the question:
> Babinet's vs. the flat model? Use them together! ;)
>
>
> thanks a lot for your reply.
>
> Could you please explain the *****physical***** meaning of using both
> models together?
I can try! Typically, we model the bulk solvent using a real space mask that is set to 1 in the bulk solvent region and 0 in the protein.
This gets Fourier transformed, symmetrized and added in to the scattering factors from the molecule (Equation 1 in the paper, page 6 in your presentation):
Ftot = Fc + ks*Fs*exp(-Bs*s^2/4)
which works great and is how things are usually coded in most macromolecular software, no problems or arguments there. However, we can come from the opposite - but equivalent! - direction of Babinet's principle, which tells us the bulk solvent can also be modeled by inverting everything: set the bulk solvent region to 0 and the protein region to 1 in the real space mask, apply a Fourier transform to that and then invert the phase:
Ftot = Fc - ks*Fm*exp(-Bs*s^2/4)
(I'm using Fm to distinguish it from Fs, due to the inversion of 0's and 1's in the real space mask) This is equation 2 in the paper.
So we're still using the flat model to compute Fm, and we're using Babinet's principle to add it in to the structure factors - although its better described as adding the inverse (thus the minus sign in the second equation) of the complement (Fm rather than Fs). These two equations are exactly equivalent, without any loss of generality. So, I would argue the flat model and Babinet's are very much congruous. Also take a look at the description/discussion in the paper regarding Figure
2 (which helped me think about things at first).
The big difference is that Babinet's is usually applied as:
Ftot = Fc - ks*Fc*exp(-Bs*s^2/4)
which, I would argue, isn't quite right - the bulk solvent doesn't scatter like protein, but it does get the shape right. Which I think is why Fokine and Urzhumtsev point out that at high resolution this form would start to show disagreement with the data. I haven't looked at this explicitly though, so we still haven't answered that question!
We didn't want to spend much time on it in the paper, our main goal was to try out the differentiable models we describe. The Babinet trick was a convenient way to make coding easier.
Anyway, I hope this helps explain it a bit more, and again: sorry for the long-windedness.
Regards,
Tim
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Tim Fenn
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Stanford University, School of Medicine
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