All - I didn't get a single response to my posting last week
(https://www.jiscmail.ac.uk/cgi-bin/webadmin?A2=ind0812&L=CCP4BB&T=0&O=D
&X=512817322E87355F7F&Y=i.tickle%40astex-therapeutics.com&P=266420)
concerning the formulae that are widely used for the 'minimally-biased'
Fourier and difference Fourier coefficients. It probably didn't help
that I posted it in the middle of the festive season! - but still
somewhat surprising since I imagine everyone here is involved with maps
at one time or another, and has an interest in getting the density that
shows best what if any further modifications need to be made to the
current model. Anyway now that people have hopefully returned to work
from the rigours of the CCP4 Study Weekend I thought I'd post it again
and see if I can provoke some discussion this time. I won't post all my
calculations again, just a summary of my conclusions.
First, I think I can now prove my conjecture that the optimal difference
Fourier coefficient dF is given for both acentrics and centrics by:
dF = Fm - DFc
where Fm is the 'minimally-biased' Fourier coefficient derived by Read
(AC 1986,A42,140):
Fm(acen) = 2mFo - DFc
Fm(cen) = mFo
I'm satisfied now that my alternative conjecture, that dF = Fm - Fc, is
probably wrong. Also I can see that there might be an argument to put
DFc in the FC (FC_ALL) column in place of Fc as appears to be currently
done by REFMAC, but not by SIGMAA (but I'd still like to see some
discussion of that).
So here's a summary comparison of theory with what is my understanding
is actually implemented in software, and with the inconsistencies
highlighted (>...<):
Source Coefficient Acentrics Centrics
====== =========== ========= ========
THEORY(Read) Fm 2mFo - DFc mFo
.. (me) dF 2(mFo-DFc) mFo - DFc
SIGMAA Fm 2mFo - DFc mFo
dF > mFo - DFc < mFo - DFc
Fc Fc Fc
REFMAC Fm 2mFo - DFc > 2mFo - DFc <
dF > mFo - DFc < mFo - DFc
Fc > DFc < > DFc <
Even if you don't accept my suggestion for the acentric dF coefficient
there are clearly some significant inconsistencies between the
coefficients output by SIGMAA & REFMAC which it would be nice to
resolve!
Cheers
-- Ian
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