Dear All,
I would like to agree with Darren. Although the drop in Rfree is
significant there are some doubts about over-fitting of the data. It is
true that theoretically complete validatation tests do prevent over-fitting but
to conserve time we do not attempt complete validation only an approximation.
Also, I think it is true that the validation technique requires that all the
measurements are independent. This is not true for reflection data.
People have said that you cannot introduce gross errors into a model
without increasing Rfree, one would hope so. However, judging whether you have
over-fitted a near correct structure this is harder to determine. Considering
that the use of geom. restraints means that the model will make chemical sense.
B-factors on the other hand are not restrained so tightly.
At the IUCr Computing School last week, Lynn Ten Eyck gave a nice talk
on least squares refinement. He performed an interesting test where he calcuated
the the eigen-vectors and eigen-values after performing full-matrix least
squares refinement on a model at different resolution ranges. When an
eigen-value drops to zero this means that a sub-set of the parameters become
undefined. It is a bit like having three unknowns but only two independent
equations. Interestingly, if one has a poor observations:pameter ratio
(like Darren) then parameters can become highly correlated and the
uncertainity in the value large. This problem of correlation decreases as
the obs.:parameter ratio increases.
I guess this answers your question about which part of the model is poorly
defined. Unfortunately, the results that Lynn presented was that the B-factors
were the parameters that first became less well defined, which is not very
helpful. I guess the real answer is to refine the model with fewer parameters.
TLS is one option that has already been suggested. The problem with TLS is
that you need to define the rigid groups in your structure. This is the
limitation of the method. I guess that something like normal modes analysis
would be an ideal tool for refinement. I believe that small molecule people
already use such programs.
Adam
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