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, fulvio.saccoc...@uniroma1.it <fulvio.saccoc...@uniroma1.it> 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 >> <fulvio.saccoc...@uniroma1.it> 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 >> >> <fulvio.saccoc...@uniroma1.it> 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 >> >> > >> > >> > >> > > > >
