Hi Fred,
On Wed, May 30, 2012 at 08:55:35AM +0200, Vellieux Frederic wrote:
> For practical purposes, a "derivative" is considered non isomorphous
> when the differences in unit cell parameters exceed ca. 1% (this is
> because if you take 2 crystals from the same crystallisation drop
> and collect and process diffraction crystals from these 2 crystals,
> you will never get exactly the very same values for the unit cell
> parameters; non-isomorphism effects start at ca. 1% change and
> you'll never get 2 perfectly isomorphous crystals - even if you
> collect diffraction data twice from the same crystals you will not
> get "perfect isomorphism").
>
> From the values mentioned, 1% of the cell parameters of the native
> for a and b is 1.81 Angstroem and for c 1.1 Angstroem (the angles do
> not matter for a trigonal space group).
>
> Had you obtained a value for a, b larger than ca. 183 Angstroem, or
> below ca. 109.2 Angstroem (only in the direction indicated by the
> changes mentioned in your mail - I ignored changes in the opposite
> direction) then you would have been able to say that the crystals
> were non-isomorphous to each other. For me they are isomorphous to
> each other and I ignore these small differences in unit cell
> parameters.
I would be careful with the (popular) percentage-rule here: the
absolute value of cell differences is much more important. At least if
we assume that the change in cell parameters roughly corresponds with
a shift in actual atoms. If you have a 1000A cell then a 1%
difference could mean a shift of 10A ... clearly, a helix moved 10A
away results in something completely different. But with a cell of 20A
you could have a 0.2A shift, which you might hardly notice.
See eg. 5.2 in Garman & Murray (2003):
http://journals.iucr.org/d/issues/2003/11/00/ba5042/index.html
which shows
5.2. Non-isomorphism
One of the biggest problems of heavy-atom derivatization is that
incorporation of a heavy atom into the lattice often induces a
change in the unit cell away from the native crystal values,
i.e. the derivatized crystal is non-isomorphous to the native
crystals. The heavy atom may perturb the arrangement of protein
molecules in the crystal or distort the protein molecule, causing
a change in unit-cell lengths. Note, however, that it is also
possible for the protein to move within the original unit cell
(resulting in a different sampling of the molecular
transform). The same unit cell is thus a necessary but not
sufficient condition for isomorphism.
Crick & Magdoff (1956[Crick, F. H. C. & Magdoff,
B. S. (1956). Acta Cryst. 9, 901-908.]) calculated that a 0.5 Å
change in all three unit-cell edges of a 100 Å cubed unit cell
would change the diffraction intensities by an average of 15% in a
3 Å resolution sphere. The predicted intensity changes induced by
non-isomorphism increase at higher resolution. When faced with a
non-isomorphous derivative, it is the absolute change in the cell
which should be considered compared with the working resolution,
rather than the relative change, i.e. a change of 1.0% in a 100 Å
unit cell edge has a similar effect to that of a 0.5% change in a
200 Å unit cell edge, if compared at similar resolutions. As a
general rule of thumb, a change in cell dimensions of dmin/4 is
tolerable, where dmin is the resolution limit (Drenth,
1999[Drenth, J. (1999). Principles of Protein X-ray
Crystallography, 2nd ed. Berlin: Springer-Verlag.]). For instance,
for 2.5 Å data, a 0.6 Å change in the unit cell might be
acceptable, whereas at 3.5 Å this could rise to 0.8 Å.
Cheers
Clemens
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