Re: Reduced spectral density mapping at three fields -- October 16, 2007 - 04:02

Hi Daniel

Calculations for the reduced spectral density mapping need only the R1, R2 and NOE at one field. R1, R2 and NOE are 3 variables you measure and you extract 3 parameters from them. This is only a simple calculation using in relax the equations that follow :

j0 = -1.5 / (3.0*d + c) * (0.5*r1 - r2 + 0.6*sigma_noe)
jwx = 1.0 / (3.0*d + c) * (r1 - 1.4*sigma_noe)
jwh = sigma_noe / (5.0*d)

where j0, jwx and jwh are, respectively, the spectral density at the zero frequency, at the nitrogen frequency (in the special case where you work with 15N relaxation) and at the apparent proton frequency (sometimes called J(wH) or J(0.87wH) ).

The other constants and variables are :

c = CSA constant
d = dipolar constant
sigma_noe = cross-relaxation rate (calculated using NOE and R1)

That said, you can extract spectral densities using data from different magnetic fields at the same time. This only changes the obtained value for J(0), as J(wN) and J(wH) are field dependent... For example, if you have data at three fields, you would get 1 value for J(0), 3 values for J(wN) and 3 values for J(wH). This approach is not yet implemented in relax, but it could be something useful. In fact, it's something I personally would like to contribute when I have time, maybe this fall...

However, calculating J(0) using different fields in separated calculations is something useful you may want to do prior to any calculation using multiple field data. The reason is that J(0) should be field independent, in cases where us-ms motions (Rex in the model-free language) are not present. Thus, calculating J(0) helps you assess the quality of your data. This is quite important as different factors may influence the consistency of your data acquired at different magnetic fields...

A part of relax is specially designed to do 3 different consistency tests : J(0), Fn and FR2. Those consistency tests are implemented in a special branch of relax which contains, apart from that, all the same functions. A sample script is also available as for other functions within relax. You can get that version of the program with svn by typing :

svn co http://svn.gna.org/svn/relax/branches/consistency_tests_1.2/ .

Some of the topics in that mail were already discussed some time ago...

You can find useful information on reduced spectral density mapping by reading the following post :

       https://mail.gna.org/public/relax-users/2006-11/msg00019.html

Also, some interesting information on consistency tests is available at :

       https://mail.gna.org/public/relax-devel/2007-06/msg00008.html


I hope this helps you out !!

Cheers


Sébastien  :)




Daniel Perez wrote:

Hi Ed,

Basic question,

relax only consider the relaxation data from one field to calculate the 
reduced spectra density mapping at three frequencies. Shouldn't one use 
at least three independent data sets (three fields) to calculate these 
three parameters.

Best Regards

Daniel

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Today's Topics:

   1. Re: Reduced spectral density mapping (Edward d'Auvergne)
   2. Re: Convergence on different systems (Edward d'Auvergne)


----------------------------------------------------------------------

Message: 1
Date: Sun, 3 Dec 2006 01:50:45 +1100
From: "Edward d'Auvergne" <edward.dauvergne@xxxxxxxxx>
Subject: Re: Reduced spectral density mapping
To: "Sebastien Morin" <sebastien.morin.1@xxxxxxxxx>
Cc: relax-users@xxxxxxx
Message-ID:
	<7f080ed10612020650v35859880kb06b327442d6fda5@xxxxxxxxxxxxxx>
Content-Type: text/plain; charset=WINDOWS-1252; format=flowed

Hi,

Reduced spectral density mapping is a direct calculation of the
spectral density values, there is no optimisation.  The only part
where optimisation could be used, but is not necessary, is in the
calculation of the single J(0) value using data at multiple field
strengths.  See Kroenke et al., 1999 for details (Kroenke, C. D.,
Rance, M. and Palmer, A. G. (1999). Variability of the 15N chemical
shift anisotropy in Escherichia coli ribonuclease H in solution. J.
Am. Chem. Soc. 121, 10119-10125).  relax can't do this yet though
(although anyone is free to add that feature).

Edward


On 12/2/06, Sebastien Morin <sebastien.morin.1@xxxxxxxxx> wrote:
  
    

Hi Edward

Thanks for your help.

I have another question about reduced spectral density mapping.

With the script jw_mapping.py, one has to select the frequency
(jw_mapping.set_frq()). I would like to know if it is possible to select
datasets at multiple fields and then optimize everything together...
Would this lead to better values as is the case with the model-free
approach ?

I tried by simply putting three fields :

===============================================================
jw_mapping.set_frq(name, frq=499.719 * 1e6, frq=599.739 * 1e6,
frq=799.744 * 1e6)
===============================================================

but as I thought, ended up with an error :

===============================================================
SyntaxError: duplicate keyword argument
===============================================================

Of course...

Thanks for help !


Séb :)
    
      

------------------------------

Message: 2
Date: Sun, 3 Dec 2006 02:02:53 +1100
From: "Edward d'Auvergne" <edward.dauvergne@xxxxxxxxx>
Subject: Re: Convergence on different systems
To: "Sebastien Morin" <sebastien.morin.1@xxxxxxxxx>
Cc: relax-users@xxxxxxx
Message-ID:
	<7f080ed10612020702w17d7e190k75b922313b2e65c8@xxxxxxxxxxxxxx>
Content-Type: text/plain; charset=ISO-8859-1; format=flowed

Convergence when using Newton optimisation in relax (or in any
application) should be quite fast.  The Newton algorithm has what is
known as quadratic convergence - the fastest type of convergence.  In
comparison steepest descent has linear convergence and the BFGS
algorithm has super-linear convergence.  For more details see, for
example, Nocedal, J. and S. J. Wright: 1999, Numerical Optimization,
Springer Series in Operations Research, New York: Springer-Verlag.
Because of the quadratic convergence, tiny parameter differences will
most likely never occur and hence the convergence tests for identical
values won't be an issue.  These tests for identical values will not
increase the amount of CPU time required relative to approximate value
tests where a small tolerance is added.

The only problem is if you continually change CPU architectures,
operating systems, etc., during the running of the 'full_analysis.py'
script.  It should be fine though if the same diffusion tensor is
optimised on the same machine.

Cheers,

Edward


On 12/2/06, Sebastien Morin <sebastien.morin.1@xxxxxxxxx> wrote:
  
    

Hi

I used the full_analysis.py script until convergence for the 4 diffusion
models (sphere, prolate, oblate, ellipsoid), each on one different
computer. Those computer, however, are quite similar, all 32-bits x86
Gentoo Linux with same kernel, gcc, python, etc.

For the final run, I switched on a different system, our dual core
pseudo 64-bits NMR console computer running Red Hat Enterprise 4 with
almost everything different from our Gentoo workstations which are
really more up-to-date. Before starting the final run, I wanted to check
if number rounding would be the same... Well, is wasn't and the run with
the ellipsoid diffusion model ended up saying it wasn't converged yet :

#####################
# Convergence tests #
#####################
Chi-squared test:
    chi2 (k-1): 7022.7261139599996
    chi2 (k):   7022.7261139563052
    The chi-squared value has not converged.
Identical model-free models test:
    The model-free models have converged.
Identical parameter test:
    Spin system: 26 PHE
    Parameter:   S2f
    Value (k-1): 0.84811676720047557
    Value (k):   0.84811676720047491
    The model-free parameters have not converged.
Convergence:
    [ No ]

As is obvious, the differences are really small, but still relax thinks
it's enough to spend many hours more trying to get absolute reproducibility.

My question.

Is it really necessary to get convergence on so small digits ? Probably
yes, as it was designed this way... So, if yes, why ? Isn't it a problem
for multi-computer processing ?

Thanks !


Séb :)


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         ______________________________________    
     _______________________________________________
    |                                               |
   || Sebastien Morin                               ||
  ||| Etudiant au PhD en biochimie                  |||
 |||| Laboratoire de resonance magnetique nucleaire ||||
||||| Dr Stephane Gagne                             |||||
 |||| CREFSIP (Universite Laval, Quebec, CANADA)    ||||
  ||| 1-418-656-2131 #4530                          |||
   ||                                               ||
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