mailRe: [bug #9259] Reduced spectral density mapping yielding bad values


Others Months | Index by Date | Thread Index
>>   [Date Prev] [Date Next] [Thread Prev] [Thread Next]

Header


Content

Posted by Sebastien Morin on June 15, 2007 - 17:43:
Hi,

Here are the different values I obtain for a residue with R1 = 1.1336 +-
0.0851 ; R2 = 12.9336 +- 0.9649 ; and NOE = 0.463921 +- 0.045


    J(0)                      J(wN)                    J(wH)
    =====================     =====================    =====================

Here are the results with Leo Spyracopoulos's Mathematica notebook.

    4.704231413115747e-9      2.664085520910741e-10    9.485555428699657e-12


Here are the results with relax without multiplying frequencies in Hz by
2 pi.

    4.6978912534878238e-09    2.6603551824374712e-10   
9.478993207668287e-12

    ratio
    0.9986522432526923179     0.9985997677461966745    
0.9993081880043085706


Here are the results with relax when multiplying frequencies in Hz by 2 pi.

    3.4634030539343071e-09    1.9612804482358541e-10   
9.478993207668287e-12

    ratio
    0.7362314371436068543     0.7361927508863804185    
0.9993081880043085706


The very small discrepancy we get (ratio 0.999...) is due to several
small differences in the definitions of constants (e.g. gn = -2.7126 in
relax and -2.7108 in Leo's notebook). This is not important. However,
there is a non negligible difference with the use of either frequencies
in Hz or frequencies transformed to rad/s.

Now, what do we do with that ?

The spectral densities are in units of rad / s = rad s^-1. (these are
not SI units, however)

The rates (R1, R2 and sigmaNOE) are in units of s^-1.

The constant 'd' is in units of s^-2.

The constant 'c' is in units of s^-2 also (or rad^2 s^-2 if we use
frequencies in rad s^-1, which are not SI units).


I now hesitate between 3 views.

1. Should the spectral densities be in SI units (i.e. in s, as the
frequencies are in s^-1 and the rates in s^-1) ?

2. If the spectral densities are in s rad^-1, the frequencies used to
calculate them should also be in rad s^-1, thus the constant 'c' should
be in rad^2 s^-2 and the constant 'd' also (so we should calculate it
without multiplying by the factor of (mu/4pi)^2). This would be about
using old units instead of the SI units, but then the spectral densities
would be in s rad^-1.

3. We could calculate everything in SI units (as we do right now) and
normalize to rs ad^-1 in the end.

Either way, I think that Leo's notebook yields spectral densities s and
not the usual s rad^-1 (as in the 2006 paper : JBNMR,36:215-224, for
which I calculated back spectral density values and yielded the same as
published where they say it's in s rad^-1, but the units deriving says
it's s).

Can you please tell me if I'm right with those ideas before I write to
Leo to report this apparent bug or typo or whatever...


Séb  :)



Edward d'Auvergne wrote:

Hi,

That is awesome work tracking down this problem.  Thank you!  I'll
apply your patch and then hopefully make a new relax 1.2 release with
your fixes very soon.  I do have a important question first though.

My question relates to the multiplication of the frequency by 2pi to
convert from Hz to rad/s units.  The symbol for the frequency in Hz is
nu whereas the frequency in rad/s is omega.  In all the relaxation
equations composed of spectral density components, the frequencies are
in rad/s and are represented by the omega symbol.  This includes the
CSA constant defined in SI units as

  c = (omegaX.CSA)^2/3,

where CSA is the chemical shift anisotropy and

  omegaX = gammaX.B0.

To get nuX which is the frequency of the X nucleus in Hz, omegaX
measured in rad/s should be divided by 2pi.  So my question is, do you
get the same results as the Mathematica notebooks of Leo Spyracopoulos
if you retain the multiplication of the frequency by 2pi?

Thanks,

Edward


P.S.  The problem with the list of frequencies is probably the major
issue.  I'm not sure why I attempted to fill out the entire list of
frequencies as the reduced spectral density mapping code only uses the
value in self.data.frq_list[0, 1], the frequency of the heteronucleus,
to calculate the CSA constant.  The higher frequencies are never used
in the calculation.  Anyway, your patch fixes this problem.




On 6/13/07, Sebastien Morin <sebastien.morin.1@xxxxxxxxx> wrote:

Hi !

I've checked the equations used for reduced spectral density mapping in
relax. They're all right... The assumption about the factor of (mu0 /
(4pi))^2 is ok since the old equations were written in Gaussian units
(cgs) and now we use SI units.

However, 2 things seem to be wrong.


1.

The frequencies need not to be scaled by a factor of 2 pi since the unit
of frequency in the SI is Hz. Thus, line 52 of 'maths_fns/jw_mapping.py'
must be removed.


2.

The frequency used for calculating the CSA seems not to be the
heteronuclear frequency. In fact, there is an error in lines 57 to 60
from 'maths_fns/jw_mapping.py' since the same item in the list is
assigned different values one after the other. Changing those lines
from :

        self.data.frq_list[0, 1] = frqX
        self.data.frq_list[0, 1] = frq - frqX
        self.data.frq_list[0, 1] = frq
        self.data.frq_list[0, 1] = frq + frqX

to :

        self.data.frq_list[0, 1] = frqX
        self.data.frq_list[0, 2] = frq - frqX
        self.data.frq_list[0, 3] = frq
        self.data.frq_list[0, 4] = frq + frqX

should work. The important thing is that item 1 stays the heteronuclear
frequency so it matches with line 1020 of 'maths_fns/ri_comps.py' :

         data.csa_const_fixed[j] = data.frq_sqrd_list[j, 1] / 3.0

where the constant 'c' is calculated using the squared heteronuclear
frequency.


With those two modifications, I now get the same values as when
calculating manually or using Leo Spyracopoulos's Mathematica notebooks
(http://www.bionmr.ualberta.ca/~lspy/index_7.html).

Bye !


Sébastien  :)





Edward d'Auvergne wrote:

Hi,

For the reduced spectral density mapping in relax, I have used
equations 10 to 12 from:

Markus M. A., Dayie K. T., Matsudaira P., and Wagner G.  Local
mobility within villin 14T probed via heteronuclear relaxation
measurements and a reduced spectral density mapping.  Biochemistry.
1996, 35(6):1722-32.

The equations themselves are derived from:

Lefevre J. F., Dayie K. T., Peng J. W., and Wagner G.  Internal
mobility in the partially folded DNA binding and dimerization domains
of GAL4: NMR analysis of the N-H spectral density functions.
Biochemistry. 1996, 35(8):2674-86.

One problem may be that I made the assumption that the dipolar
constant of equation 7 of the first reference was missing the factor
of (mu0 / (4pi))^2!  I based this assumption on the SI units
formulation of the R1, R2, and NOE equations and how the CSA constant
is defined.  I think this is a fairly safe assumption though if you
look at equations 1, 2, and 8 of that paper.

Could the problem be the definition of the equations used?  I've
looked at the code in relax and it seems to replicate these equations
correctly.  Are the equations of Markus et al., (1996) correct?  Is my
assumption about the dipolar constant correct?  If you manually
calculate the reduced spectral density values using these alternative
equations, does relax produce the same values?  I'm sorry that I can't
exactly pinpoint the problem, but something is seriously amiss.

Regards,

Edward




On 6/1/07, anonymous <NO-REPLY.INVALID-ADDRESS@xxxxxxx> wrote:


URL:
  <http://gna.org/bugs/?9259>

                 Summary: Reduced spectral density mapping

yielding bad

values
                 Project: relax
            Submitted by: None
            Submitted on: Friday 06/01/2007 at 17:15 CEST
                Category: relax's source code
                Severity: 4 - Important
                Priority: 5 - Normal
                  Status: None
                 Privacy: Public
             Assigned to: None
         Originator Name: Sébastien Morin
        Originator Email: sebastien.morin.1@xxxxxxxxx
             Open/Closed: Open
         Discussion Lock: Any
                 Release: Repository: 1.2 line
        Operating System: GNU/Linux

    _______________________________________________________

Details:

Hi

I performed spectral density mapping on data recorded at three

magnetic

fields (500, 600, 800).

The values I get are erroneous (when compared with Leo Spyracopoulos'
Mathematica notebook which were manually verified using equations
from the
method 1 of Farrow et al., 1995, JBNMR, 6 : 153) and scaled depending
on the
magnetic field as shown in the table below (for which values
calculated using
either Leo's notebook or relax are divided by the value calculated
manually).

Field    Method    J(0)          J(wN)         J(wH)
=====    =======   ==========    ==========    ==========
500      Farrow    1 (ref)       1 (ref)       1 (ref)
         Leo       1             1             1
         relax     0.04758       0.04757       0.999

600      Farrow    1 (ref)       1 (ref)       1 (ref)
         Leo       1             1             1
         relax     0.03361       0.03361       0.999

800      Farrow    1 (ref)       1 (ref)       1
         Leo       1             1             1
         relax     0.01932       0.01932       0.999

Then, if you take the different values for J(0) and J(wN) and compare
from
field to field, you get this :

              J(0)      J(wN)     J(wH)
              ========  ========  ========
500/600 ->    1.415     1.415     1
500/800 ->    2.462     2.462     1

Those ratios are similar to what you get when comparing fields
quadratically
:

(600/500)^2 = (1.2)^2 = 1.44 ~ 1.415
(800/500)^2 = (1.6)^2 = 2.56 ~ 2.462

So there seems to be a problem somewhere in the calculations of

J(0) and

J(wN) and, to a lesser extent, J(wH)...

I first thought the problem was related with bug #9238... In fact,
before
this bug was solved, the problem was worst by a factor of ~2...
Still, the
skewing of Jw mapping results is quite important. Maybe is this
something
with the units or constants values...

Thanks for helping me !


Sébastien :)






    _______________________________________________________

Reply to this item at:

  <http://gna.org/bugs/?9259>

_______________________________________________
  Message sent via/by Gna!
  http://gna.org/


_______________________________________________
relax (http://nmr-relax.com)

This is the relax-devel mailing list
relax-devel@xxxxxxx

To unsubscribe from this list, get a password
reminder, or change your subscription options,
visit the list information page at
https://mail.gna.org/listinfo/relax-devel






-- 
         ______________________________________
     _______________________________________________
    |                                               |
   || 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                          |||
   ||                                               ||
    |_______________________________________________|
         ______________________________________







-- 
         ______________________________________    
     _______________________________________________
    |                                               |
   || 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                          |||
   ||                                               ||
    |_______________________________________________|
         ______________________________________

Related Messages


Powered by MHonArc, Updated Tue Jun 19 12:20:35 2007