I've seen this estimate of the determinancy point for torsion angle
refinement presented by Axel Brunger at ACA meeting this summer.  I
don't remember all the details, but no, it did not refer to the approach
described in the paper where higher resolution model is used as a
restraint.  It was simply done by equalizing the number of torsions in
the protein of certain molecular weight and number of reflections
obtained at certain resolution assuming certain solvent content.  His
point (assuming that I understood it correctly) was that when you are
working with 5A data your are definitely at the limit where even
torsional refinement may become underdetermined.  Thus you need more
restraints, and it seems that you may be able to get them from higher
resolution structures of, say, subunits of the same protein.

You make an excellent point about the histogram - just because it's in
PDB doesn't mean it's right.  I've seen 2A structures there with waters
that had hydrogens, but I won't condone that :)

On Wed, 2009-09-23 at 10:31 -0500, Pete Meyer wrote:
> > Brunger, A., DeLaBarre, B., Davies, J. & Weis, W. X-ray structure
> > determination at low resolution. ACTA CRYSTALLOGRAPHICA SECTION
> > D-BIOLOGICAL CRYSTALLOGRAPHY 65, 128-133 (2009).  
> > 
> > The paper quotes Wayne Hendrickson (says "submitted") regarding
> > "determinancy" point (i.e. where the number of observations becomes
> > equal to the number of flexible torsions (of course, in this extreme
> > case gemoetric restraints essentially become constraints and you don't
> > refine B-factrors at all.  With 50% solvent this is ~5.4A, and you are
> > far from that limit.
> 
>  From a quick glance at that paper (although not the "submitted" one), 
> it looks like this determinancy point may only apply to cases where 
> components from high resolution structures are being used at lower 
> resolution (independent components of a complex at high res vs the full 
> complex at low res).  This may or may not apply to cases where an 
> initial model refined at higher resolution is not available, although 
> I'm leaning more towards the "not applicable" side at the moment (my 
> understanding was that some level of over-determination was required. 
> Exactly what minimum level of over-determination is required is 
> something I haven't been able to find out yet).
> 
> > It is rather surprising that any reviewer anywhere would have doubts
> > about possibility to refine structural model at 3.4A.  While I don't
> > know what the referee said *exactly*, but he/she may be unaware of this
> > 
> > http://www.rcsb.org/pdb/statistics/histogram.do?mdcat=refine&mditem=ls_d_res_high&minLabel=0&maxLabel=5&numOfbars=10&name=Resolution
> 
> At 3.4 Angstroms, refinement should definitely be possible.  But I might 
> not point a reviewer at that histogram.  Assuming "mdcat=refine" is 
> limiting results to entries that have been refined, that table has 
> entries in the 20 to 70 Angstrom range, where I'd have doubts about the 
> validity of any refinement done.  So I'm not sure that the PDB is 
> filtering for cases of acceptable refinement vs any refinement at all 
> (I've seen REMARK lines in deposited entries where the authors reported 
> that the refinement statistics were not necessarily valid given the 
> resolution of the structure; it may be easier to do a few cycles of 
> refinement to satisfy deposition requirements than deposit an unrefined 
> structure at low resolution).
> 
> > 
> > 
> > 
> > On Wed, 2009-09-23 at 12:48 +0000, hugh morgan wrote:
> >> Hi, 
> >>     We are attempting to address a referees comment concerning our
> >> data/parameter ratio for a 3.4 A structure. Although the ratio is only
> >> 0.5, the R/Rfree is 25/29, which seems acceptable. Ideally I would
> >> like to include a reference showing a graph or table of data:parameter
> >> vs resolution but I have been unable to find such a paper. Please
> >> could someone point me in the right direction. 
> >> Thanks in advance
> >>
> >> Hugh
> >>
> >> P.S. It would be nice to know if this table has been published
> >> http://www-structmed.cimr.cam.ac.uk/Course/Basic_refinement/Refinement.html
> >>
> >> or something similar to this, which includes higher resolution
> >> structures
> >> http://dirac.cnrs-orleans.fr/plone/Members/hinsen/data-parameter-ratio-in-x-ray-structure-determination
> >>
> >>
> >>
--