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 <[email protected]> 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 >
