Dear Ian & other CCP4ers,
I want to get a riddle about counting geometrical restraints solved,
which emerged in my head after a recent discussion
<http://www.mail-archive.com/ccp4bb@jiscmail.ac.uk/msg17534.html> on
this board about the effect of NCS on the data:parameter ratio. This
discussion quickly centered around the 1998 Acta Cryst paper about
R-factor ratios [1]. So, here is my riddle:
On one hand, geometrical restraints can be counted as observations.
Refinement programs use differences between model geometry and ideal
geometry restraints as least-squares targets, in a similar way to
differences between model structure factor amplitudes and observed
structure factor amplitudes. Model refinement is possible using
geometrical restraints only, in the complete absence of observed
structure factor amplitudes (idealization; whether this makes sense, is
a different question). Geometrical restraints are also counted as
observations in [1], both in Table 1 and in the text (for example in
formula 2).
On the other hand, it is shown in that paper, summarized in Table 2,
that for the Rfree/Rwork ratios, geometrical restraints effectively
reduce the number of refinement parameters, with a smooth transition
from restraints to constraints via the residual term Drest. This implies
that geometrical restraints can be counted as reducing the numbers of
parameters, not as increasing the number of observations, which was also
brought up as an argument in the aforementioned discussion.
Thus, on one hand, geometrical restraints can be counted as
observations, on the other hand they can be counted as reducing the
number of parameters. The riddle for me is, that these two ways of
counting are mutually exclusive alternatives - so, which one is the
right one?
I would be grateful, if you, Ian, or any other crystallographer on this
board could help me (and maybe others) to solve this riddle.
Best regards,
Dirk.
[1] Tickle, Laskowski, Moss. "Rfree and the rfree ratio. I. Derivation
of expected values of cross-validation residuals used in macromolecular
least-squares refinement", Acta Cryst., D54, 547-557 (1998)
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Dirk Kostrewa
Gene Center Munich, A5.07
Department of Biochemistry
Ludwig-Maximilians-Universität München
Feodor-Lynen-Str. 25
D-81377 Munich
Germany
Phone: +49-89-2180-76845
Fax: +49-89-2180-76999
E-mail: kostr...@genzentrum.lmu.de
WWW: www.genzentrum.lmu.de
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