Hi, The following is a copy of my post to the NESSY mailing list at https://mail.gna.org/public/nessy-users/2014-03/msg00001.html. This replicated here on the relax-users mailing list to be used as a permanent relax reference (parts of it might be copied into the relax wiki or manual in the future). If you are interested in relaxation dispersion, you might find the concepts useful for understanding the Hertz vs. 1/s vs. rad/s vs. radian Hertz base units, especially for the kex exchange parameter. Below is the verbatim copy of the text.
Regards, Edward P. S. Here is the text with a few minor corrections: Hi Henriette, Welcome to the NESSY mailing lists! The problem you are seeing here is not very well understood - even by the top experts in the field. Many people are confused by the concept and it often results in mistakes in papers. To explain this, I will use the following resources which I recommend that you read: 1) The relaxation dispersion chapter of the user manual for the software relax (http://www.nmr-relax.com) has a comprehensive table listing all conceivable dispersion parameters and their base units (http://download.gna.org/relax/manual/relax.pdf). An online version of the table can be seen at http://www.nmr-relax.com/manual/Dispersion_model_summary.html. 2) The hidden radian unit concept which I have explained at http://wiki.nmr-relax.com/Hidden_radian_units. 3) The unit analysis for the relaxation equations at http://thread.gmane.org/gmane.science.nmr.relax.devel/1023/focus=1034. A similar unit analysis can be performed for kex, which I have performed but not published or written anywhere. This analysis works for all models showing kex to have rad/s units, except for the IT99 model (http://wiki.nmr-relax.com/IT99). 4) The software comparison table I produced for relax which compares numerical results from most of the dispersion software available in the field. This is available with relax in the file ./test_suite/shared_data/ dispersion/software_comparison or online at http://svn.gna.org/viewcvs/*checkout*/relax/trunk/test_suite/shared_data/dispersion/software_comparison?revision=21873. So, to begin, rad/s and 1/s are almost always the same thing in NMR as almost everything we look at is rotational. This is due to the hidden radian unit concept (ref. 2). Note that 1/s and Hz in NMR are most definitely not the same thing and you need a factor of 2pi to convert between them. Just as a side note, 1/s is properly called radian Hertz though this is not often used in the field. By convention, parameters with rad/s units are often called omega whereas parameter with Hertz units are called nu. Chemical exchange relates to chemical shift, which is the change in how a nucleus spins in a magnetic field. The spinning means that chemical shift is a rotational process (which interacts with the non-rotational external magnetic field and induced magnetic fields for the electrons in the system, though these have rotational fluctuations in the structural reference frame due to Brownian and internal motions). The Rex term which contributes to relaxation hence has the units of rad/s. This matches the units of R1, R2, and sigma_NOE (see ref. 3), as well as the spectral density functions governing standard relaxation. In the case of kex, this is where a lot of confusion arises. The reason is because kex has both rad/s and Hertz units - there are actually two kex parameters. The first is the one which influences the chemical shift - this has the radian unit. The second is the translational component of the mechanical process causing exchange - the kinetic parameter of the process - this is non-rotational and hence has Hertz units. There is no factor of 2pi when converting between the two! A rotational process in rad/s or radian Hertz can interact directly with a non-rotational process in Hertz with no conversion factors. For relaxation dispersion we assume both kex are the same. Therefore it is technically correct to present the single numeric value with both 1/s and Hertz units (as well as rad/s and radian Hertz units). There is a case where kex can have rad^2 units but I won't get into that (the rad^2/s units are mentioned at https://en.wikipedia.org/wiki/Rotational_diffusion). For a quick unit analysis, the CR72 dispersion model for CPMG-type data is a simple starting point (http://wiki.nmr-relax.com/CR72). >From section 10.3.3 of the relax manual: R2eff = 1/2 (R20A + R02B + kex - 2*nu_CPMG*cosh^-1 (D+*cosh(eta+) - D-*cos(eta-))). The units of R2eff, R20A, and R20B are by definition rad/s. Therefore to add kex directly to these, kex must also have rad/s units (unit analysis of the last term also produces rad/s, but I won't go into that as it's too long). For the M61 model for R1rho-type data (http://wiki.nmr-relax.com/M61 and section 10.7.1 of the relax manual): R1rho = R1rho' + phi_ex*kex / (kex^2 + omega_e^2), where: phi_ex = pA*pB*delta_omega^2. Here both phi_ex and omega_e have the units of rad^2/s^2. To add kex^2 to omega_e^2, it must also have rad^2/s^2 units. The denominator therefore has rad^2/s^2 units. The numerator has (rad^2/s^2 * rad/s) units, or rad^3/s^3 units. Dividing the numerator and denominator, we have (rad^3/s^3 / (rad^2/s^2)). This can be seen to cancel to rad/s units. This matches the base units for R1rho' and R1rho which are also rad/s units by definition. Such a unit analysis can be performed for all analytic and numeric dispersion models and kex will always have rad/s units (IT99 is a bizarre exception). I hope some of this information helps. But if you look at ref. 4, you will see all dispersion software compared produce the same numerical kex value. There are no errors in NESSY, relax, CPMGFit, cpmg_fit, or ShereKhan due to missing factors of 2pi. There are errors/differences due to other problems, but that's a different story. Regards, Edward P. S. For a more detailed comparison of different relaxation dispersion software, see section 10.12 "Comparison of dispersion analysis software" of the relax manual (http://download.gna.org/relax/manual/relax.pdf). On 26 March 2014 09:49, Henriette Molinari <henriette.molin...@univr.it> wrote: > Dear Nessy authors, > we have an enormous and important doubt. > Looking at your equations and to the supplementary files found in your > "help" menu, > it appears that kex units, deriving from NESSY fitting analysis, are rad/sec > AND NOT 1/sec. > This means that all the extracted kex should be multiplied by 2pi. > Could you confirm this point? > It is crucial as we are publishing a review comparing different kex values > reported in the literature > for a class of protein, and this point is extremely important. > > I apologise if my question is trivial, however I find literature very > confusing on this subject > > Thank you so much > > With best regards > Henriette Molinari > > > > Prof. Henriette Molinari > ISMAC CNR Milano, Via Bassini 15, > 20133 Milano > cell. 3290594246 phone 0223699724 > President GIDRM _______________________________________________ relax (http://www.nmr-relax.com) This is the relax-users mailing list relax-users@gna.org 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-users
