Dale, On Tue, May 4, 2010 at 12:19 AM, Dale Tronrud <det...@uoxray.uoregon.edu> wrote: > The greater the difference in cell constants the greater the "noise" > in the map. I think the high resolution cutoff for the maps should > be > > 2 A delta/(A+delta) > > where A is the cell edge with the largest change, and delta is the > amount of change (in Angstrom). Basically a 1A change for a 100A > edge would require a 2A resolution limit. A 5A change would imply > a 10A cutoff and a very boring map.
I think this estimate may be a little over-optimistic. Crick & Magdoff (1956, Acta Cryst.9, 901–908) calculated that for a 100Å cubic unit cell a 0.5% change in all the cell dimensions, or a 0.5° rotation of the molecule within the unit cell, would produce an average 15% change in intensity, equivalent to a 7.5% average change in F, for data to 3Å resolution. So your 1% change in cell at 2Å would give ~ 22.5% average change in F, just from the non-isomorphism effects. For an Fo-Fc map, given that measurement errors are typically ~ 4 or 5% in F, you need to have the average difference due the ligand or heavy atom at least 3 times the noise level at the bare minimum, say at least 12%, and indeed we see average differences (i.e. partial Fc) due to a soaked ligand in the range 10-20%. For an Fo-Fo map the noise level is multiplied by sqrt(2) since you have 2 lots of measurement errors, so you have 6-8% average experimental error in Fo-Fo. Now clearly if you have experimental errors of ~ 7% plus non-isomorphism errors of 22.5% and you're looking for a signal of 15% due to the ligand then you have a problem! It implies you need to reduce the non-isomorphism errors by a factor of at least 3, i.e. to <= 0.3% change in cell at 2Å. Such a stringent requirement, which is virtually impossible to achieve for frozen/soaked crystals (freezing & soaking can easily induce > 1% and sometimes > 5% change), is surely the reason that Fo-Fo maps never caught on! One objection to this that I've seen is that Fo-Fc differences include errors due to the model, say ~ 20% (assuming that's the R factor), which Fo-Fo differences clearly do not. However the point is that this 20% contribution from the model error is spread throughout the cell, not just at the ligand site, since it arises from co-ordinate & B factor errors, disorder etc in all atoms, of which the ligand makes up a very small fraction, so the contribution to this from errors in the ligand parameters are likely to be negligible (adding the ligand has a negligible effect on the R factor!). In contrast the ~ 5% experimental error in Fo-Fc, or ~ 7% + non-isomorphism error for Fo-Fo, contribute roughly equally to the error in the density over the whole cell. Cheers -- Ian
