In this section, the user can select a model for fitting the data based on a chosen exchange regime.
The fittings presume the following kinetic scheme:
The following formulas are used to calculate R2,eff for different models such as the Bloch-McConnell [1], Carver-Richards [2, 3] and Luz-Meiboom [4] models:
Bloch-McConnell model |
![Model_matrix](/assets/help/model_matrix-0dce3e0579a56c4dd184a005a1f30ceb.png) |
Carver-Richards model |
![Model_london](/assets/help/model_london-247c48bd0f4d1569225a18008b194f96.png) |
Luz-Meiboom model |
![Model_meiboom](/assets/help/model_meiboom-884a8e14c36eb535a636cf7cb297cada.png) |
where |
TCP | given constant relaxation delay |
![Vcpmg](/assets/help/vcpmg-8c388c626f133422db2bada7102a691f.png) | given CPMG frequency |
B0 | given field strength for the nuclei of the interest in MHz |
| |
R2 | fitted intrinsic transverse relaxation rate |
kAB, kBA | fitted kinetic rate constants (slow exchange) |
kex | fitted kinetic rate constant (fast exchange) |
Δδ | fitted chemical shift difference in ppm (slow exchange) |
φ | fitted population weighted chemical shift difference in ppm2 (fast exchange) |
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The optimization of the parameters is performed by minimizing the target function:
where |
![R2efexp](/assets/help/R2efexp-44f5769e81c46cf54e1078772070d030.png) | given experimental relaxation rate |
![Oexp](/assets/help/oexp-b001a2ed98334ab4506547da83079fa7.png) | given experimental error in the relaxation rate |
![R2efclc](/assets/help/R2efclc-bebe1b2f93e8267c16833d10a3756259.png) | calculated relaxation rate based on model |
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References
[1] | McConnell, H. M. (1958) Reaction rates by nuclear magnetic resonance, J. Chem. Phys. 28, 430- 431 |
[2] | Davis, D.G. et al. (1994) Direct measurements of the dissociation-rate constant for inhibitor-enzyme complexes via the T1 rho and T2 (CPMG) methods. J. Magn. Reson. B, 104, 266–275. |
[3] | Carver, J. P.; Richards, R. E. (1972) General 2-site solution for chemical exchange produced dependence of T2 upon Carr-Purcell pulse separation J. Magn. Reson., 6, 89-96. |
[4] | Luz, Z. and Meiboom, S. (1963) Nuclear Magnetic Resonance study of the protolysis of trimethylammonium ion in aqueous solution—order of the reaction with respect to solvent. J. Chem. Phys., 39, 366–370. |