Dear Peter,
Thank you for posting this info to the relax mailing lists. It is
much appreciated. I hadn't thought too much about this, but this is
as you say: an error propagation through a ratio. The same occurs
within the steady-state NOE error calculation. As y=1/B and errA=0,
we could simply take the PDC file data and convert the error as:
sigma_R1 = sigma_T1 / T1^2.
This would be a 100% exact error calculation. Therefore within relax,
we will only need to read the final relaxation data from the PDC files
and nothing about the peak intensities. Reading additional
information from the PDC files could be added later, if someone needs
that. One thing that would be very useful would be to have higher
precision values and errors in the PDC files. 5 or more significant
figures verses the current 2 or 3 would be of great benefit for
downstream analyses. For a plot this is not necessary but for high
precision and highly non-linear analysis such as model-free (and SRLS
and spectral density mapping), this introduces significant propagating
truncation errors. It would be good to avoid this issue.
An additional question is about the error calculation within the
Protein Dynamics Centre. For model-free analysis, the errors are just
as important or maybe even more important than the data itself. So it
is very important to know that the errors input into relax are of high
quality. Ideally the R1 and R2 relaxation rate errors input into
relax would be from the gold standard of error propagation - Monte
Carlo simulations. Is this what the PDC uses, or is the less accurate
jackknife technique used, or the even lowest accuracy covariance
matrix estimate? And how are replicated spectra used in the PDC? For
example, if only a few time points are duplicated, if all time points
are duplicated, if all time points are triplicated (I've seen this
done before), or if no time points are duplicated. How does the PDC
handle each situation and how are the errors calculated? relax
handles these all differently, and this is fully documented at
http://www.nmr-relax.com/api/1.3/prompt.spectrum.Spectrum-class.html#error_analysis.
Also, does the PDC use peak heights or peak volumes to measure signal
intensities?
Sorry for all the questions, but I have one more. All of the
fundamental NMR theories work in rates (model-free, SRLS, relaxation
dispersion, spectral density mapping, Abragam's relaxation equations
and their derivation, etc.), and most of the NMR dynamics software
accepts rates and their errors and not times. The BMRB database now
will also accept rates in their new version 3.1 NMR-STAR definition
within the Auto_relaxation saveframe. Also most people in the
dynamics field publish R1 and R2 plots, while T1 and T2 plots are much
rarer (unless you go back to the 80's). If all Bruker users start to
publish Tx plots while most of the rest publish Rx plots, comparisons
between different molecular systems will be complicated. So is there
a specific reason the PDC outputs in relaxation times rather than in
rates?
Cheers,
Edward
On 16 November 2010 06:52, Neidig Klaus-Peter
<Klaus-Peter.Neidig@xxxxxxxxxxxxxxxxx> wrote:
Dear all, Dear Michael & Edward,
I'm currently on the way to England, thus only a short note:
The error or an inverse is a special case of the error of a ratio. A search
for "error propagation" in the internet yields
hundreds of hits. There are also some discussions about correlation
bewtween involved quantities.
If y=A/B with given errors of A and B then the absolute error of y is y *
sqrt [(errA/errB)^2 + (errB/B)^2]
If A=1 you get error of y is y*errB/B, since the error of a constant is 0.
I compared the results with the errors I got from Marquardt if I fit a*
exp(-Rt) instead of a* exp(-t/T) by eye up to
a number of digits.
I hope, I did it right.
Best regards,
Peter
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