I'll happily add my name to the consensus! However it's interesting
to consider why some rotation functions are frankly uninterpretable
and some, as George says, are spectacular. In fact the major cause of
failure of MR has been known for a long time; in a word:
incompleteness. The reason is obvious: the effect of omitting a
reflection from the Patterson function is the same as adding to the
true Patterson the Fourier term corresponding to the negative
intensity of the omitted reflection, and of course if that intensity
happens to be large then it's hardly surprising that it has a
deleterious effect. Of course you won't know whether or not it's
large - because obviously it's not there in processed dataset!
There's a golden rule of experimental data collection: never throw
away data - if you do it's likely to come back to bite you!
Usually the problem is having a few strong low resolution reflections
missing due to detector overloads or backstop occlusion, though this
situation is improving as the dynamic range of modern detectors gets
bigger. I don't think backstops have improved much though - in the
old days to avoid getting a backstop shadow we used to make one by
gluing a piece of lead (obviously as small as possible while still
blocking the beam) to a strip of sticky tape. I guess you're probably
not allowed to do that any more! Having a whole shell of reflections
missing can be equally problematic, which is why it's probably a good
idea to use all available data in a self-rotation function; for a
cross-rotation function of course there are other issues to consider
such as the expected similarity of the model and target structures.
Something I've always thought would be useful is for the image
integration programs to set an error status instead of rejecting an
overloaded/overlapped/occluded reflection, since obviously for MR any
estimate of an intensity which is less than the true intensity is
better than no estimate (ice spots, zingers etc could be a problem
though). Then the user has the option to include the reflection in
MR: obviously for refinements and difference maps where what matters
is essentially the difference between the observed & calculated
amplitudes you would want to omit reflections flagged with an error
status. I suspect that the problem of getting agreement on the form
of the error status between the various programmers means this idea
will never get off the ground!
One explanation of why using Es sometimes helps is that the missing
overloads will mostly be at low resolution and Es of course
down-weight the low-res data (including the missing ones!). There's
an article I wrote for the CCP4 newsletter many years ago where we
showed that the rotation function is very sensitive to a very small
number of missing large reflections (maybe only 1 or 2% of the total),
but that this sensitivity is reduced if Es are used.
Cheers
-- Ian
On Mon, Mar 22, 2010 at 11:37 AM, George M. Sheldrick
<[log in to unmask]> wrote:
> I have to agree with Clemens and Eleanor. After I had come to the wrong
> conclusion about NCS and the number of molecules in the asymmetric unit
> several times I gave up using the self-rotation function. Nevertheless,
> I have been shown examples (especially NCS with Cn symmetry and unsual n)
> where the self-rotation function was spectacular.
>
> George
>
> Prof. George M. Sheldrick FRS
> Dept. Structural Chemistry,
> University of Goettingen,
> Tammannstr. 4,
> D37077 Goettingen, Germany
> Tel. +49-551-39-3021 or -3068
> Fax. +49-551-39-22582
>
>
> On Mon, 22 Mar 2010, Eleanor Dodson wrote:
>
>> I absolutely agree with Clemens; self rotation functions can mislead in some
>> cases, and confuse in many more.. A peak in a self rotation does NOT mean you
>> have a dimer or a trimer - just that one molecule in the asu can be related to
>> another by the given operator. So for any peak ther are nsym*2 possible
>> positions..
>>
>> However old fashioned programs like polarrfn, almn, and amore list all
>> symmetry equivalents of each peak which often illuminate things, and you often
>> notice that the expected 3-fold generates 2 folds when combined with symmetry
>> operators.
>>
>> You dont give the angles of your 3 fold, but if phi=45, omega = 36, the
>> combination with crystallography 2 folds generates non-crystallographic
>> two-folds in the a-b plane..
>> Eleanor
>>
>> Clemens Vonrhein wrote:
>> > Hi Francis,
>> >
>> > On Thu, Mar 18, 2010 at 09:03:13AM -0600, Francis E Reyes wrote:
>> > > Hi all
>> > >
>> > > I have a solved structure that crystallizes as a trimer
>> >
>> > I guess you mean that you have 3 mol/asu? And not just "a trimer in
>> > solution that then forms crystals", right?
>> >
>> > > to a reasonable R/Rfree, but I'm trying to rationalize the peaks in
>> > > my self rotation.
>> >
>> > That has very often fooled me: selfrotation functions can be very
>> > misleading - at least in my hands (even using different programs,
>> > resoluton limits, E vs F etc etc). Often peaks that should be there
>> > aren't and vice versa.
>> >
>> > > The space group is P212121, calculating my self
>> > > rotations from 50-3A, integration radius of 22 (the radius of my
>> > > molecule is about 44). I can see the three fold NCS from my
>> > > structure on the 120 slice
>> >
>> > Which one is it: the one at (90,90) or the one at (45,45)?
>> >
>> > Or both?
>> >
>> > > but I'm trying to rationalize apparent two folds in my kappa=180. A
>> > > picture of both slices is enclosed. The non crystallographic peaks
>> > > for kappa=180, P222 begin to appear at kappa=150 and are strongest
>> > > on the 180 slice.
>> >
>> > If you had a D_3 multimer (3-fold with three 2-folds perpendicular to
>> > it) I could interpret those as
>> >
>> > (a) 3-fold at (90,90)
>> >
>> > ==> 2-fold at ( 90,0) [direction cosines = 1.00000 0.00000 0.00000]
>> > 2-fold at (210,0) [direction cosines = -0.50000 -0.00000
>> > -0.86603]
>> > 2-fold at (330,0) [direction cosines = -0.50000 -0.00000
>> > 0.86603]
>> >
>> > (b) 3-fold at (45,45)
>> >
>> > ==> 2-fold at ( 90,315) [direction cosines = 0.70711 -0.70711 0.00000]
>> > 2-fold at ( 45,180) [direction cosines = -0.70711 0.00000
>> > 0.70711]
>> > 2-fold at (135, 90) [direction cosines = 0.00000 0.70711
>> > -0.70711]
>> >
>> > All those 2-folds axes have a 120-degree angle between them (obviously).
>> >
>> > I might have the exact angles wrong (there could be slight offsets
>> > from thoise ideal values and the self-rotation plot just piles the
>> > peaks exactly onto crystallographic symmetry operators because of the
>> > multiplicity of those symmetry elements) ... or maybe even more? But
>> > for both 3-fold axes in the kappa=120 section I can convince myself
>> > that there are the corresponding 2-folds to make up a D_3 multimer.
>> >
>> > Since you probably only have space for 3 mol/asu, I would guess case
>> > (a) to be the correct 3-fold NCS with the 2-folds in (a) resulting
>> > from the 21 parallel to your 3-fold and the peaks in (b) resulting
>> > from the remaining symmetry.
>> >
>> > Does that fit?
>> >
>> > Cheers
>> >
>> > Clemens
>> >
>> > > My molecule looks close to a bagel (44A wide and 28A tall). The
>> > > three fold NCS is down the axis of looking down on the bagel
>> > > hole. I'm trying to find the two fold. I imagine it could be slicing
>> > > the bagel in half (like to eat it for yourself) or slicing it
>> > > vertically (like to share amongst kids) but I'm not exactly sure
>> > > what's the best way to visualize this. Is there something easier
>> > > than correlation maps with getax (since I have the rotation
>> > > (polarrfn) and translation?). If you have an eye for spotting
>> > > symmetry, Ill send the pdb in confidence.
>> >
>> > > Thanks!
>> > >
>> > > FR
>> > >
>> > >
>> >
>> >
>> >
>> > > ---------------------------------------------
>> > > Francis Reyes M.Sc.
>> > > 215 UCB
>> > > University of Colorado at Boulder
>> > >
>> > > gpg --keyserver pgp.mit.edu --recv-keys 67BA8D5D
>> > >
>> > > 8AE2 F2F4 90F7 9640 28BC 686F 78FD 6669 67BA 8D5D
>> > >
>> > >
>> > >
>> >
>> >
>>
>
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