Hi Tim,
sorry for my late reply - I just came back to the lab.
In the Babinet bulk solvent correction, no bulk solvent phases are used,
it is entirely based on amplitudes and strictly only valid if the phases
of the bulk solvent are opposite to the ones of the protein. And as
Sasha Urzhumtsev pointed out, this assumption is only valid at very low
resolution.
The mask bulk solvent correction is a vector sum including the phases of
the bulk solvent mask, which makes a difference at medium resolution (up
to ~4.5 A, or so).
As far as I can see, your formulas given below do not distinguish
between amplitude (modulus) and vector bulk solvent corrections.
Personally, I really don't see any physical sense in using both
corrections together, except for compensating any potential scaling
problems at low resolution.
If the model is basically complete and correct, the mask bulk solvent
correction is usually superior to the Babinet bulk solvent correction
(see, for example, my old and small CCP4 Newsletter contribution
<http://www.ccp4.ac.uk/newsletters/newsletter34/bsdk_text.html>).
However, there are also good reasons for using the Babinet bulk solvent
correction (it should be an option in ALL refinement programs!):
- it requires only two parameters and can be used in any case
- in rigid body refinement, the mask lags behind; here, I always use the
Babinet BS correction
- channels could show false positive density, because the mask left them
empty - this depends heavily on the choice of radii to determine/shrink
the bulk solvent mask; in such cases, I always calculate a Babinet BS
correction as a control
Best regards,
Dirk.
Am 23.10.10 22:14, schrieb Tim Fenn:
On Sat, 23 Oct 2010 10:05:15 -0700
Pavel Afonine<pafon...@gmail.com> 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
--
*******************************************************
Dirk Kostrewa
Gene Center Munich, A5.07
Department of Biochemistry
Ludwig-Maximilians-Universität München
Feodor-Lynen-Str. 25
D-81377 Munich
Germany
Phone: +49-89-2180-76845
Fax: +49-89-2180-76999
E-mail: kostr...@genzentrum.lmu.de
WWW: www.genzentrum.lmu.de
*******************************************************
