Hi Florian,
Tight NCS restraints or NCS constraints (they are essentially the same
thing in effect if not in implementation) both reduce the effective
parameter count on a 1-for-1 basis.
Restraints should not be considered as being added to the pool of
X-ray observations in the calculation of the obs/param ratio, simply
because restraints and X-ray observations can in no way be regarded as
interchangeable (increasing the no of restraints by N is not
equivalent to increasing the no of reflections by N). This becomes
apparent when you try to compute the expected Rfree: the effective
contribution of the restraints has to be subtracted from the parameter
count, not added to the observation count.
The complication is that a 'weak' restraint is equivalent to less than
1 parameter (I call it the 'effective no of restraints': it can be
calculated from the chi-squared for the restraint). Obviously no
restraint is equivalent no parameter, so you can think of it as a
continuous sliding scale from no restraint (effective contribution to
be subtracted from parameter count = 0) through weak restraint (0 <
contribution < 1) through tight restraint (count ~=1) to constraint
(count = 1).
Cheers
-- Ian
On Sat, Sep 18, 2010 at 9:23 PM, Florian Schmitzberger
<[log in to unmask]> wrote:
> Dear All,
>
> I would have a question regarding the effect of non-crystallographic
> symmetry (NCS) on the data:parameter ratio in refinement.
>
> I am working with X-ray data to a maximum resolution of 4.1-4.4 Angstroem,
> 79 % solvent content, in P6222 space group; with 22 300 unique reflections
> and expected 1132 amino acid residues in the asymmetric unit, proper 2-fold
> rotational NCS (SAD phased and no high-resolution molecular replacement or
> homology model available).
>
> Assuming refinement of x,y,z, B and a polyalanine model (i.e. ca. 5700
> atoms), this would equal an observation:parameter ratio of roughly 1:1. This
> I think would be equivalent to a "normal" protein with 50 % solvent content,
> diffracting to better than 3 Angstroem resolution (from the statistics I
> could find, at that resolution a mean data:parameter ratio of ca. 0.9:1 can
> be expected for refinement of x,y,z, and individual isotropic B; ignoring
> bond angle/length geometrical restraints at the moment).
>
> My question is how I could factor in the 2-fold rotational NCS for the
> estimate of the observations, assuming tight NCS restraints (or even
> constraint). It is normally assumed NCS reduces the noise by a factor of the
> square root of the NCS order, but I would be more interested how much it
> adds on the observation side (used as a restraint) or reduction of the
> parameters (used as a constraint). I don't suppose it would be correct to
> assume that the 2-fold NCS would half the number of parameters to refine
> (assuming an NCS constraint)?
>
> Regards,
>
> Florian
>
> -----------------------------------------------------------
> Florian Schmitzberger
> Biological Chemistry and Molecular Pharmacology
> Harvard Medical School
> 250 Longwood Avenue, SGM 130
> Boston, MA 02115, US
> Tel: 001 617 432 5602
>
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