Substituting zero vs. Fc for unobserved reflections

From: Gregg Crichlow
Date: 27 March 2012 21:06

Please excuse me for bringing up an old issue.  I have an interesting example of a difference seen when DFc was substituted for missing reflections versus when it wasn't. Maybe others had this experience.  I had a structure in which the electron density showed two 'overlapping' ligands bound in the same active site.  One was the ligand that was co-crystallized with the protein.  The other was the same ligand but with an unintentional modification (presumably due to radiation dose).  I was able to discern the two forms in the electron density (1.55 A) being that they did not completely overlap.  Based on occupancy refinement, the occupancies were 0.12 and 0.88 (unmodified and modified forms, respectively).  Then one time I calculated the map using a second program, and the lower occupancy ligand disappeared!  When I calculated maps in the first program, there were again two forms visible.  I thought that the difference may be due to the difference between substituting unobserved reflections with Fc (or rather DFc because of sigma-A weighting) versus omitting them from the Fourier transform.  The program that kept showing me two forms bound was not substituting Fcalc for unobserved reflections.  So, I turned on the option to substitute Fcalc, and the minor form disappeared – the density looked like it did in the second program.  I figured the density that reveals the two forms must be correct being that it would be a big coincidence for artifactual density to appear that just so happens to fit perfectly ouradded (unmodified)ligand at 1.55 A.  So, I suppose, being that the occupancy of the major form is so much higher, by substituting unobserved reflections with Fcalc, the major form is being overemphasized, and the minor form becomes invisible.

                  There may be many cases in which substituting Fcalc (or DFc) for missing reflections is beneficial. I don't know the mathematical or theoretical arguments behind it.  I'm not arguing for one way being generally superior to the other, or for one program over another.  However, this is one empirical example of it being advantageous not to make this substitution.

                  When calculating experimentally phased maps, we multiply our structure factors by a figure of merit to down-weight reflections with less certain phases. Could one consider leaving missing reflections as zero analogous to multiplying Fcalc by FOM = 0? (just asking – maybe this is faulty logic.) Of course, this would be for the sake of the amplitude instead of the phase in this case. If an intensity is not observed, we have the ultimate uncertainty regarding its value.

Maybe some developers will want to use this structure and the corresponding data to test DFc vs. "0" vs. DFc multiplied by a specific FOM only used for the missing reflections, varying from 0 to 1.  Unfortunately, this structure is not yet published (we needed to wait for other experiments to be finished) so I cannot yet provide it or the structure factors. However, if anyone is interested, feel free to contact me, and when it is published I would behappy to let you know the PDB code, if you still want it.

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Gregg Crichlow

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From: Ethan Merritt


[Snipped from the full message, which is appended below]

> The program that kept showing me two forms bound was not
> substituting Fcalc for unobserved reflections.  So, I turned on the option
> to substitute Fcalc, and the minor form disappeared � the density looked
> like it did in the second program.  I figured the density that reveals the
> two forms must be correct being that it would be a big coincidence for
> artifactual density to appear that just so happens to fit perfectly our
> added (unmodified)ligand at 1.55 A.  So, I suppose, being that the occupancy
> of the major form is so much higher, by substituting unobserved reflections
> with Fcalc, the major form is being overemphasized, and the minor form
> becomes invisible.

A weighted difference map (mFo - DFc) that does not include the ligand
atoms in Fc at all would be a better guide.  It would not be biased by
the current ligand model [or at least much less biased] and it certainly
would not be sensitive to the modelled occupancies since these atoms
would not be contributing to Fc at all regardless of occupancy.

It is in general more convincing to show difference density from
an Fo-Fc map with ligands omitted from Fc than it is to show density
from some variant of 2Fo-Fc with ligands included in Fc.

How complete is your data set?
Are you trying to deal with more than a few per cent of missing reflections?
If it is only the highest resolution shell that has poor completeness,
have you tried truncating the map calculation to a shell that is complete?

       Ethan

> would be happy to let you know the PDB code, if you still want it.

--
Ethan A Merritt

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From: Craig Bingman


I would be concerned about the completeness of the data if adding Fcalc values has such a large effect on the appearance of this electron density.

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From: Gregg Crichlow

Thank you for your responses. Actually, the data are very complete: 99.6% total and 99.2% in the high resolution shell. Only 2% of data were used for cross validation because there were a large number of reflections.

I had calculated omit maps. At first when I discovered the presence of the lower occupancy form, I initially only had the modified ligand in the map, but then using phases from the model including it, noticed extra density explainable by the unmodified ligand. Afterward, however, I calculated omit maps, removing all ligands. The mFo-DFc omit map does indeed show features of the unmodified (lower occupancy) ligand even when omitting all ligands in the model. However, the 2mFo-Dfc omit map shows the lower occupancy form better than the mFo-Dfc omit map.  Interesting.

Gregg

 

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Gregg Crichlow