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 wasn¹t. Maybe others had this experience. I had
a structure in which the electron density showed two overlapping¹ 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 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.
There may be many cases in which substituting Fcalc (or
DFc) for missing reflections is beneficial. I don¹t know the mathematical or
theoretical arguments behind it. I¹m 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. ³0² 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 be happy to let you know the PDB code, if you still want it.
*******************************************
Gregg Crichlow
Dept. of Pharmacology
Yale University
P.O. Box 208066
New Haven, CT 06520-8066
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