This is a subtle problem and performing an analysis of this type of error is confusing. Most of the tools we use to analyze errors begin with the assumption that the "errors" are random and uncorrelated. These include Luzzati and Fo-Fc maps.
My solution is to perform a null hypothesis test. If you run two refinements starting from the same model, in one allowing the RB shift and in the other forbidding it, which fits the data better? If the difference in likelihood is quite small then you cannot distinguish between a RB shifted model and one w/o the shift and that shift must be insignificant (in a statistical sense.) If the likelihood is better when the shift is allowed then the shift is significant. In my experience RB shifts of a couple tens of an Angstrom are very significant even with 4 A resolution data. X-ray diffraction is exquisitely sensitive to this sort of motion. Dale Tronrud On 11/21/11 14:52, Filip Van Petegem wrote: > Hello Jacob, > > that's correct, I'm only looking at the mathematical significance, not > the biological one. I follow the same reasoning - it is highly > improbably for all atoms to be skewed in the same direction. > > In a case I'm currently looking at, I'm particularly dealing with > cryo-EM data, not X-ray structures, but with the same underlying > principles: what are the odds that all pixels of the map move together > in the same direction? > > As mentioned for X-ray structures, a Luzzati analysis may give > information about the positional errors, but there should be an > increased resolution when comparing domain movements, because it's > unlikely for all atoms to have an error in the same direction. > > Filip > > On Mon, Nov 21, 2011 at 2:16 PM, Jacob Keller > <j-kell...@fsm.northwestern.edu <mailto:j-kell...@fsm.northwestern.edu>> > wrote: > > Just to clarify: I think the question is about the mathematical sense > of "significance," and not the functional or physiological > significance, right? If I understand the question correctly, wouldn't > the reasoning be that admittedly each atom in the model has a certain > positional error, but all together, it would be very unlikely for all > atoms to be skewed in the same direction? > > Jacob > > > > On Mon, Nov 21, 2011 at 4:04 PM, Filip Van Petegem > <filip.vanpete...@gmail.com <mailto:filip.vanpete...@gmail.com>> wrote: > > Dear crystallographers, > > I have a general question concerning the comparison of different > > structures. Suppose you have a crystal structure containing a > few domains. > > You also have another structure of the same, but in a different > condition > > (with a bound ligand, a mutation, or simply a different > crystallization > > condition,...). After careful superpositions, you notice that one > of the > > domains has shifted over a particular distance compared to the other > > domains, say 1-1.5 Angstrom. This is a shift of the entire > domain. Now > > how can you know that this is a 'significant' change? Say the overall > > resolution of the structures is lower than the observed distance > (2.5A for > > example). > > Now saying that a 1.5 Angstrom movement of an entire domain is not > relevant > > at this resolution would seem wrong: we're not talking about some > electron > > density protruding a bit more in one structure versus another, but > all of > > the density has moved in a concerted fashion. So this would seem > 'real', > > and not due to noise. I'm not talking about the fact that this > movement > > was artificially caused by crystal packing or something similar. > Just for > > whatever the reason (whether packing, pH, ligand binding, ...), > you simply > > observe the movement. > > So the question is: how you can state that a particular movement was > > 'significantly large' compared to the resolution limit? In > particular, what > > is the theoretical framework that allows you to state that some > movement is > > signifcant? This type of question of course also applies to other > methods > > such as cryo-EM. Is a 7A movement of an entire domain > 'significant' in a > > 10A map? If it is, how do we quantify the significance? > > If anybody has a great reference or just an individual opinion, > I'd like to > > hear about it. > > Regards, > > Filip Van Petegem > > > > -- > > Filip Van Petegem, PhD > > Assistant Professor > > The University of British Columbia > > Dept. of Biochemistry and Molecular Biology > > 2350 Health Sciences Mall - Rm 2.356 > > Vancouver, V6T 1Z3 > > > > phone: +1 604 827 4267 <tel:%2B1%20604%20827%204267> > > email: filip.vanpete...@gmail.com <mailto:filip.vanpete...@gmail.com> > > http://crg.ubc.ca/VanPetegem/ > > > > > > -- > ******************************************* > Jacob Pearson Keller > Northwestern University > Medical Scientist Training Program > email: j-kell...@northwestern.edu <mailto:j-kell...@northwestern.edu> > ******************************************* > > > > > -- > Filip Van Petegem, PhD > Assistant Professor > The University of British Columbia > Dept. of Biochemistry and Molecular Biology > 2350 Health Sciences Mall - Rm 2.356 > Vancouver, V6T 1Z3 > > phone: +1 604 827 4267 > email: filip.vanpete...@gmail.com <mailto:filip.vanpete...@gmail.com> > http://crg.ubc.ca/VanPetegem/
