mailRe: Diffusion Tensor - Global correlation time


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Posted by Chris MacRaild on October 05, 2006 - 10:58:
On Thu, 2006-10-05 at 03:11 +1000, Edward d'Auvergne wrote:
Hi,

That is good question.  I have to warn you though that my opinion is
going to be very heavily biased!  Essentially the way that model-free
analysis has been implemented over the last 17 years or so (since the
publication of Kay et al., 1989) is as follows:

1.  Estimate the Brownian rotational diffusion tensor.
2.  Hold the diffusion tensor fixed and optimise each model-free model.
3.  Model-free model selection (in my opinion this is best done using
AIC model selection ;).
4.  Optimisation of the diffusion tensor parameters together with the
parameters of the selected model-free model.
5.  Repeat the steps, using the final optimised diffusion tensor as
the starting point of the next iteration, until 'convergence'.

On top of this I have recently proposed an additional step prior to
'model-free model selection' called 'model-free model elimination' to
remove failed model-free models.  The most common way of carrying out
step 1 is to use the R2/R1 ratio (Kay et al., 1989).  relax can not
only implement this data analysis chain but, due to it's modularity
and flexibility, it can also implement many of the different published
variations to this approach.

There is a sample script called 'full_analysis.py' distributed with
relax which implements a radically different approach to Kay's
paradigm.  Rather than starting with the diffusion tensor and ending
with the model-free parameters, this new model-free optimisation
protocol applies this logic in reverse.  It starts by optimising the
model-free models and finishes by optimising the diffusion tensor.
The benefits of this approach is that it avoids the pitfalls of
obtaining the initial diffusion tensor estimate, avoids the hidden
motion problem (Orekhov et al., 1995, Orekhov et al., 1999a, Orekhov
et al., 1999b), and avoids under-fitting (which causes artificial
motions to appear).

I presented this new protocol on a poster at the 2006 ICMRBS
conference in Goettingen and I currently have a number of submitted
manuscripts which, unfortunately, are not published yet.  These papers
will demonstrate the application and performance of the new model-free
optimisation protocol.  However all the steps of the analysis are
described in fine detail at the start of the 'full_analysis.py'
script.

Sorry about all that biased, unpublished opinion.  In summary relax
can be used to implement most of the data analysis protocols in the
literature.  I hope that answers your question.

Edward


References:
Kay, L. E., Torchia, D. A., and Bax, A. (1989) Biochem. 28(23), 8972-8979.
Orekhov, V. Y., Korzhnev, D. M., Diercks, T., Kessler, H., and
Arseniev, A. S. (1999a) J. Biomol. NMR 14(4), 345-356.
Orekhov, V. Y., Korzhnev, D. M., Pervushin, K. V., Hoffmann, E., and
Arseniev, A. S. (1999b) J. Biomol. Struct. Dyn. 17(1), 157-174.
Orekhov, V. Y., Pervushin, K. V., Korzhnev, D. M., and Arseniev, A. S.
(1995) J. Biomol. NMR 17(1), 157-174.



I can add my observations, from spending much time hitting my head against 
these problems in a few different systems. I find that Lewis Kay's 
approach and Edward's new proposal (the 'full_analysis.py' approach) work
well for differing systems. For very good data, both work well and
converge on the same result. For data has a few 'outliers' (eg. residues
affected by Rex or complex ns motions) Kay's approach can fail because
the initial estimate of the diffusion constant is not good enough. On
the other hand, Edward's approach seems more robust to these types
outliers, but in my hands sometimes requires a very precise data set in
order to converge. One clear benefit of Edward's approach is that
failure is obvious - it simply doesn't converge on a diffusion ternsor,
and chi2 eventually starts to rise as the tensor drifts into the wrong
area. On the other hand, judging the success of the Kay approach can be
much more difficult.

In conclusion, my advice is to try both approaches on a carefully pruned
dataset - it is well worth spending time on getting this right first up,
because everything else depends on it.

Hope this helps,

Chris




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