Thanks Ian,
I understood now.
Great lesson for me.
Best regards
Fulvio Saccoccia
Il giorno ven, 20/05/2011 alle 18.14 +0100, Ian Tickle ha scritto:
> The true values of the components of the twin can't in general be
> equal since they come from _different_ reflections that are unrelated
> by the true crystal symmetry (they are only related by the
> pseudo-symmetry of the twin).
>
> Let's say:
>
> Itwin(h1)=tf*I(h1)+(1-tf)*I(h2)
>
> where I(h1) and I(h2) are the true intensities of the reflections h1
> and h2 related by the twin operator. h1 and h2 are reflections that
> are _un_related by the true symmetry operators, i.e. they are
> different reflections so do not in general have the same intensity.
>
> and
>
> Itwin(h2)=tf*I(h2)+(1-tf)*I(h1)
>
> is the twinned intensity of the reflection related to Itwin(h1) by the
> twin operator.
>
> If and only if tf = 0.5 then we have:
>
> Itwin(h1)=0.5*(I(h1)+I(h2))
>
> Itwin(h2)=0.5*(I(h2)+I(h1))
>
> which are obviously equal. So it's the intensities in the _twin_ that
> become equal when tf=0.5, NOT the true intensities (these obviously
> remain the same whether it's twinned or not).
>
> Multiplying all the intensities by the same scale factor cannot
> possibly have any effect on the Wilson B factor, since the intensities
> are in any case on an arbitrary scale. For example the diffracted
> intensity is proportional to the incident intensity, so the
> intensities will be on a different scale depending on where you
> collected the data (also the size of the collimator, thickness of
> crystal, thickness of attenuator, type of mirror focusing, beam
> current etc etc). Clearly none of these factors can possibly
> influence the B factor, which is an inherent property of the crystal
> structure,
>
> Strictly if you multiply I by a factor you must multiply sigma(I) by
> the same factor (since I/sigma(I) must stay the same), maybe this is
> the problem. A simpler one-step way to halve I and sigma(I) is to use
> sftools, that's how I would do it. Maybe something went wrong in your
> procedure.
>
> Cheers
>
> -- Ian
>
> On Fri, May 20, 2011 at 5:43 PM, [log in to unmask]
> <[log in to unmask]> wrote:
> > Thanks Ian,
> > but your reply confused me a little.
> > I hope you can explain me where I was wrong.
> >
> > I know that
> >
> > I(twin)=tf*I(h1)+(1-tf)*I(h2)
> >
> > I supposed that having tf=0.5 I could take the I(twin), dividing by 2 I
> > will get both I(h1) and I(h2), that are the two component (that are
> > equal in this case).
> >
> > Rather I thought that a possible mistake could be the sigI associated to
> > every intensities ( and I don't know how I can take it into account for
> > Wilson B).
> >
> > Just to tell you and review the procedure I followed: I took the .sca, I
> > operated in order to halve the Intensities column (I used octave to
> > calculate them), saved the new file in .txt and than I applied label FP
> > and SIGFP using F2mtz (ccp4i). After this, I run wilson (ccp4) within
> > 30-3,0 A resolution and obtain a more reliable B factor with respect
> > that obtained from raw data that was of 3A^2. Next, I tried changing the
> > resolution 30-4.5 and 30-4.4 and the results are all similar (28, 31 and
> > 38 A^2). The SCALE were 186 204 and 194 and I considered them quite
> > similar one to another.
> >
> > I did not made this procedure in order to detwin data just to understand
> > how "play" with raw data affected by perfect twin and to clarify me how
> > these data affect statistics.
> >
> >
> >
> > Thank you for your attention and for all the good advice.
> >
> > Cheers
> >
> > Fulvio
> >
> > Il giorno ven, 20/05/2011 alle 16.26 +0100, Ian Tickle ha scritto:
> >> No, simply applying a single overall scale factor to the intensities
> >> can't possibly make any difference to the Wilson B since the fall-off
> >> with resolution will remain unchanged. The Wilson plot is a plot of
> >> ln(mean(I')/S) in shells of constant d* vs d*^2, where I' is I
> >> corrected for symmetry and S is a function of the scattering factors
> >> for the known unit cell content. Changing the overall scale factor
> >> shifts the plot up or down but doesn't change the gradient, and the
> >> Wilson B factor depends on the gradient (actually B = -2*gradient).
> >>
> >> In any case detwinning is impossible if as you say the twin fraction
> >> is near 0.5. Your procedure doesn't perform detwinning. For example,
> >> suppose the true intensities of the components of the twin are (say)
> >> 90 and 110. For tf = 0.5 you will observe the mean value (i.e. half
> >> from each component), so I(twin) = 100. Taking I(twin)/2 = 50 doesn't
> >> give you back the true intensity (in fact in this case I(twin) is
> >> actually a better estimate of I(true)); in any case any attempt at
> >> detwinning must give you 2 values, one for each component of the twin.
> >>
> >> Cheers
> >>
> >> -- Ian
> >>
> >> On Fri, May 20, 2011 at 3:43 PM, fulvio saccoccia
> >> <[log in to unmask]> wrote:
> >> > Thanks Ian,
> >> > I tried to do this:
> >> > I took the file containing
> >> > hkl I and sigI
> >> >
> >> > and generated a new file containing
> >> >
> >> > hkl I/2 and sigI
> >> >
> >> > because I know, from the refined structure that the twin fraction is
> >> > nearly 0.5. Now, using this new file the wilson plot give me a more
> >> > reliable estimated B factor.
> >> >
> >> > Do you think this procedure was correct?
> >> >
> >> > Fulvio
> >> >
> >> > Il giorno gio, 19/05/2011 alle 14.14 +0100, Ian Tickle ha scritto:
> >> >> Hi Fulvio
> >> >>
> >> >> There are 2 different issues here: the Wilson plot scale & B factor on
> >> >> the one hand and Wilson statistics on the other. The first are not
> >> >> affected by twinning since they depend only on the intensity averages
> >> >> in shells. The second refers to the distribution of intensities (i.e.
> >> >> the proportion of reflections with intensity less than a specified
> >> >> value) within a shell, or to the distribution of normalised
> >> >> intensities (Z = I/<I> ignoring symmetry issues for now) over the
> >> >> whole dataset. This distribution is different for a twin because
> >> >> averaging the components which contribute to the intensity of a
> >> >> twinned reflection tends to shift the distribution towards the mean,
> >> >> so you get fewer extreme values.
> >> >>
> >> >> The Wilson B factor is not a 'statistic' in the strict sense, merely a
> >> >> derived parameter. I suspect the low value you get has more to do
> >> >> with the fact that the resolution is only 3 A, than the fact it's
> >> >> twinned.
> >> >>
> >> >> See here for more mathematically-oriented info:
> >> >>
> >> >> http://www.ccp4.ac.uk/dist/html/pxmaths/bmg10.html
> >> >>
> >> >> Cheers
> >> >>
> >> >> -- Ian
> >> >>
> >> >> On Thu, May 19, 2011 at 1:45 PM, fulvio saccoccia
> >> >> <[log in to unmask]> wrote:
> >> >> > Dear ccp4 users,
> >> >> > I have a data set arising from a nearly-perfect pseudo-merohedrally
> >> >> > twinned cystal, diffracting up to 3 A. I solved the structure and ready
> >> >> > for deposition, but there is still a trouble.
> >> >> > The Wilson scaling from raw data gave a B of 3A^2.
> >> >> > Initially, I did not seemed too alarming. But I do not know why I have
> >> >> > these statistics.
> >> >> >
> >> >> > Does anyone know why Wilson scaling falls when treating that kind of
> >> >> > twinned data? I read that twinned data do not obey twe Wilson statistics
> >> >> > but I don't know why.
> >> >> > Here the presentation I read:
> >> >> >
> >> >> > http://bstr521.biostr.washington.edu/PDF/Twinning_2007.pdf
> >> >> >
> >> >> > Do you know any articles, reviews or book in which this particular
> >> >> > aspect of of twinned data is treated in depth, possibly in mathematical
> >> >> > manner?
> >> >> >
> >> >> > Thanks to all
> >> >> >
> >> >> > Fulvio Saccoccia, PhD student
> >> >> > Biochemical Sciences Dept.
> >> >> > Sapienza University of Rome
> >> >> >
> >> >
> >> >
> >> >
> >
> >
> >
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