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On Aug 24, 2006, at 2:08 AM, Dirk Kostrewa wrote:
Here, I disagree: as you stated above, the model should make
physically and chemically sense. If you allow a larger deviation
from expected chemistry only because the lower resolution of the
observed data doesn't allow for a more precise model, you will
violate that physical/chemical reasoning. The underlying problem
is, as Gerard has pointed out, that there is no good single model
that would explain low resolution data. In principle, one should
describe these data with multiple models, but this is prohibitive
given the low amount of data. I also think that the best that one
can currently do with low resolution data is to use a single model
tightly restrained to expected chemistry together with TLS to
describe at least partially the model's rigid body flexibility.
Here is a different way of describing the thought:
There is dynamic disorder of every atom, there is static disorder
(i.e. atoms sit at slightly different positions within the unit
cell), and there are crystal imperfections (missing/tilted unit
cells, etc.). If we were to superimpose every unit cell and plot the
position of every atom, we would find that the atomic positions have
a wide spread. By calculating the geometric center for every unique
atom, we get what one could call the "crystal structure". This is an
average structure. If we now calculate bond lengths and angles, we
will find that they vary a lot with respect to ideal values. However,
this is physically and chemically perfectly reasonable, because we
are looking at an AVERAGE structure, not the structure of a single
molecule. Determination of the atomic positions would be driven by R/
Rfree, and the esd's and deviations of the geometric parameters from
ideal values would tell us something about the degree of disorder. We
could stop here and say, "This is a crystal structure. It is an
average structure, and the rmsd's therefore look a bit funky. Live
with it!" So, if we are fitting an average structure, we should have
large target values for the rmsd's, i.e. we should allow for large
deviations from ideality, particularly at low resolution, i.e. for
badly disordered crystals.
But we don't stop there. We ask, "What is that single structure that
is ideal in terms of geometry and that also best fits to the
determined atomic positions?" Here, it does make sense to use a model
that is indeed very tight if not even constrained in large parts, so
that physical reality is observed. That reality should not be
different at different resolutions. Refinement is driven by
minimizing deviations from ideality; R factors will increase, but so
what. So, if we are asking for a single structure, it should have
should have small target values for the rmsd's, i.e. small deviations
from ideality.
In practice, we are using a mixed approach, and that is what gets us
into trouble, because we are comparing geometric parameters of some
sort of average to ideal values. As long, however, as we know what
"good" target values are, and as long as the rest of the scientific
community doesn't get confused, we should have no problem. Sadly,
neither seems to be the case.
Now, it is not at all prohibitive to calculate multiple structures,
even at low resolution. Provided the number of fitted parameters was
chosen appropriately, we could simply ask, "What are ALL the
structures that are ideal in terms of geometry and that also best fit
to the determined atomic positions?" Just like NMR people do it. We
can simply run many independent refinements using simulated
annealing, or some other randomizer, and calculate all structures
that are within kT or some other criterion. We would not violate any
data/parameter ratio rules, because we are not refining the
structures simultaneously. Every single structure would still be
ideal in terms of geometry, and all structures taken together as an
ensemble would well describe the (averaged) crystal structure. We
would then use rmsd's to describe deviations between all ideal
structures that fit the data, just like in NMR, and get rid of the
confusing rmsd's for bond lengths and angles.
Misconceptions?
------------------------------------------------------------------------
--------
Mischa Machius, PhD
Associate Professor
UT Southwestern Medical Center at Dallas
5323 Harry Hines Blvd.; ND10.214A
Dallas, TX 75390-8816; U.S.A.
Tel: +1 214 645 6381
Fax: +1 214 645 6353
