Exchange regime and exchange model

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
Carver-Richards model Model_london
Luz-Meiboom model Model_meiboom
TCPgiven constant relaxation delay
Vcpmggiven CPMG frequency
B0given field strength for the nuclei of the interest in MHz
R2fitted intrinsic transverse relaxation rate
kAB, kBAfitted kinetic rate constants (slow exchange)
kexfitted kinetic rate constant (fast exchange)
Δδfitted chemical shift difference in ppm (slow exchange)
φfitted population weighted chemical shift difference in ppm2 (fast exchange)

The optimization of the parameters is performed by minimizing the target function:

R2efexpgiven experimental relaxation rate
Oexpgiven experimental error in the relaxation rate
R2efclccalculated relaxation rate based on model


[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.