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, [email protected] > <[email protected]> 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 > >> <[email protected]> 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 > >> >> <[email protected]> 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 > >> >> > > >> > > >> > > >> > > > > > > >
