Subsections

Dispersion model summary

Except for `R2eff' and `No Rex', all models can be fit to clusterings of spins, or spin blocks. The models are described in more detail below and summarised in Table 11.1. The parameters of the models and of relaxation dispersion in general are given in Table 17.5.

R1 parameter optimisation

For a number of models, the off-resonance R1 value can be optimised. Normally the off-resonance models will use fixed experimental R1 values for optimisation. However if the experimental values are not loaded, then the R1 values will be automatically optimised. For finer control of this optimisation behaviour, see the relax_disp.r1_fit user function (page [*]). The models which support off-resonance R1 fitting include:

In the future, support for off-resonance effects in the CPMG experiments is planned (see section 11.10 on page [*]).

Table 11.1: The dispersion models supported by relax.

Model name Solution Sites Parameters Restrictions Reference

Experiment independent
R2eff - - {R2eff, ... } Fixed relaxation time period -
R2eff - - {R2eff, I0, ... } Variable relaxation time period -
No Rex Closed 1 {R20, ... } - -
CPMG-type
LM63 Analytic 2 {R20,..., Φex, kex} Fast exchange Luz and Meiboom (1963)
LM63 3-site Analytic 3 {R20,..., Φex, B, kB, Φex, C, kC} Fast exchange, pA > pB and Luz and Meiboom (1963)
pA > pC
CR72 Analytic 2 {R20,..., pA, Δω, kex} pA > pB, not very slow exchange Carver and Richards (1972)
CR72 full Analytic 2 {R2A0, R2B0,..., pA, Δω, kex} pA > pB, not very slow exchange Carver and Richards (1972)
IT99 Analytic 2 {R20,..., pA, Δω, τex} pA $ \gg$ pB Ishima and Torchia (1999)
TSMFK01 Analytic 2 {R2A0,..., Δω, kAB} pA $ \gg$ pB slow exchange Tollinger et al. (2001)
B14 Analytic 2 {R20,..., pA, Δω, kex} pA > pB, Baldwin (2014)
B14 full Analytic 2 {R2A0, R2B0,..., pA, Δω, kex} pA > pB, Baldwin (2014)
NS CPMG 2-site expanded Numeric 2 {R20,..., pA, Δω, kex} pA > pB Tollinger et al. (2001)
NS CPMG 2-site 3D Numeric 2 {R20,..., pA, Δω, kex} pA > pB -
NS CPMG 2-site 3D full Numeric 2 {R2A0, R2B0,..., pA, Δω, kex} pA > pB -
NS CPMG 2-site star Numeric 2 {R20,..., pA, Δω, kex} pA > pB -
NS CPMG 2-site star full Numeric 2 {R2A0, R2B0,..., pA, Δω, kex} pA > pB -
MMQ CPMG-type
MMQ CR72 Analytic 2 {R20,..., pA, Δω, ΔωH, kex} pA > pB Korzhnev et al. (2004a)
NS MMQ 2-site Numeric 2 {R20,..., pA, Δω, ΔωH, kex} pA > pB Korzhnev et al. (2005a)
NS MMQ 3-site linear Numeric 3 {R20,..., pA, pB, ΔωAB, ΔωBC, pA > pB and pB > pC Korzhnev et al. (2005a)
ΔωHAB, ΔωHBC, kexAB, kexBC}
NS MMQ 3-site Numeric 3 {R20,..., pA, pB, ΔωAB, ΔωBC, pA > pB and pB > pC Korzhnev et al. (2005a)
ΔωHAB, ΔωHBC, kexAB, kexBC, kexAC}
R1ρ-type
M61 Analytic 2 {R1ρ',..., Φex, kex} Fast exchange, on-resonance, Meiboom (1961)
R1 = R2
DPL94 Analytic 2 {R1ρ',..., Φex, kex} Fast exchange Davis et al. (1994)
M61 skew Analytic 2 {R1ρ',..., pA, Δω, kex} pA $ \gg$ pB, on-resonance Meiboom (1961)
TP02 Analytic 2 {R1ρ',..., pA, Δω, kex} pA $ \gg$ pB, not fast exchange Trott and Palmer (2002)
TAP03 Analytic 2 {R1ρ',..., pA, Δω, kex} Weak condition of pA $ \gg$ pB Trott et al. (2003)
TP0411.1 Analytic N {R1ρ',..., p1,..., pN,$ \overline{{\omega}}$, k12,... k1N} One site dominant Trott and Palmer (2004)
MP05 Analytic 2 {R1ρ',..., pA, Δω, kex} pA > pB Miloushev and Palmer (2005)
BK13 Analytic 2 {R20,..., pA, Δω, kex} pA > pB, Baldwin and Kay (2013)
BK13 full Analytic 2 {R2A0, R2B0,..., pA, Δω, kex} pA > pB, Baldwin and Kay (2013)
NS R1rho 2-site Numeric 2 {R1ρ',..., pA, Δω, kex} pA > pB -
NS R1rho 3-site linear Numeric 3 {R1ρ',..., pA, pB, ΔωAB, ΔωBC, pA > pB and pA > pC -
kexAB, kexBC}
NS R1rho 3-site Numeric 3 {R1ρ',..., pA, pB, ΔωAB, ΔωBC, pA > pB and pA > pC -
kexAB, kexBC, kexAC}

Table 11.2: The parameters of relaxation dispersion.

Parameter Equation Description Units

νCPMG

1/(4τCPMG) CPMG frequency Hz
τCPMG 1/(4νCPMG) Delay between CPMG π pulses s
Trelax - The relaxation delay period s
I0 - Reference peak intensity when Trelax is zero -
I1 - Peak intensity for a given νCPMG or spin-lock field strength ω1 -
R20 - R2 relaxation rate in the absence of exchange rad.s-1
R2A0 - R2 relaxation rate for state A in the absence of exchange rad.s-1
R2B0 - R2 relaxation rate for state B in the absence of exchange rad.s-1
R1ρ' - R1ρ relaxation rate in the absence of exchange rad.s-1
$ \overline{{\Omega}}$ $ \overline{{\omega}}$ - ωrf The average resonance offset in the rotating frame rad.s-1
ΩA ωA - ωrf The resonance offset in the rotating frame for state A rad.s-1
ΩB ωB - ωrf The resonance offset in the rotating frame for state B rad.s-1
ΩC ωC - ωrf The resonance offset in the rotating frame for state C rad.s-1
ωA - The Larmor frequency of the spin in state A rad.s-1
ωB - The Larmor frequency of the spin in state B rad.s-1
ωC - The Larmor frequency of the spin in state C rad.s-1
ωHA - The proton Larmor frequency of the spin in state A (for MMQ data) rad.s-1
ωHB - The proton Larmor frequency of the spin in state B (for MMQ data) rad.s-1
ωHC - The proton Larmor frequency of the spin in state C (for MMQ data) rad.s-1
$ \overline{{\omega}}$ pAωA + pBωB The population averaged Larmor frequency of the spin rad.s-1
ω1 - Spin-lock field strength, i.e. the amplitude of the rf field rad.s-1
ωe $ \sqrt{{\overline{\Omega}^2 + \omega_1 ^2}}$ Effective field in the rotating frame rad.s-1
ωrf - Spin-lock offset, i.e. the frequency of the rf field rad.s-1
θ arctan$ \left(\vphantom{ \frac{\omega_1 }{\overline{\Omega}} }\right.$$ {\frac{{\omega_1 }}{{\overline{\Omega}}}}$$ \left.\vphantom{ \frac{\omega_1 }{\overline{\Omega}} }\right)$ Rotating frame tilt angle rad
kAB pBkex The forward exchange rate from state A to state B (2-site) rad.s-1
kBA pAkex The reverse exchange rate from state B to state A (2-site) rad.s-1
kAB pBkexAB The forward exchange rate from state A to state B (3-site) rad.s-1
kBA pAkexAB The reverse exchange rate from state B to state A (3-site) rad.s-1
kBC pCkexBC The forward exchange rate from state B to state C (3-site) rad.s-1
kCB pBkexBC The reverse exchange rate from state C to state B (3-site) rad.s-1
kAC pCkexAC The forward exchange rate from state A to state C (3-site) rad.s-1
kCA pAkexAC The reverse exchange rate from state C to state A (3-site) rad.s-1
kex 1/τex Chemical exchange rate constant rad.s-1
kexAB kAB + kBA Chemical exchange rate constant between sites A and B rad.s-1
kexBC kBC + kCB Chemical exchange rate constant between sites B and C rad.s-1
kexAC kAC + kCA Chemical exchange rate constant between sites A and C rad.s-1
kB $ \approx$ kexAB Approximate chemical exchange rate constant between sites A and B rad.s-1
kC $ \approx$ kexAC Approximate chemical exchange rate constant between sites A and C rad.s-1
τex 1/kex Time of exchange s.rad-1
pA - Population of state A -
pB 1 - pA Population of state B (2-site) -
pB 1 - pA - pC Population of state B (3-site) -
pC 1 - pA - pB Population of state C (3-site) -
Δω ωB - ωA Chemical shift difference between sites A and B (2-site) rad.s-1 (stored as ppm)
ΔωAB ωB - ωA Chemical shift difference between sites A and B (3-site) rad.s-1 (stored as ppm)
ΔωBC ωC - ωB Chemical shift difference between sites B and C (3-site) rad.s-1 (stored as ppm)
ΔωAC ΔωAB + ΔωBC Chemical shift difference between sites A and C (3-site) rad.s-1 (stored as ppm)
ΔωH ωHB - ωHA Proton chemical shift difference between sites A and B (2-site) rad.s-1 (stored as ppm)
ΔωHAB ωHB - ωHA Proton chemical shift difference between sites A and B (3-site) rad.s-1 (stored as ppm)
ΔωHBC ωHC - ωHB Proton chemical shift difference between sites B and C (3-site) rad.s-1 (stored as ppm)
ΔωHAC ΔωHAB + ΔωHBC Proton chemical shift difference between sites A and C (3-site) rad.s-1 (stored as ppm)
Φex pApBΔω2 Fast exchange factor rad2.s-2 (stored as ppm2)
Φex, B See 11.20a on page [*] Fast exchange factor between sites A and B rad2.s-2 (stored as ppm2)
Φex, C See 11.20b on page [*] Fast exchange factor between sites A and C rad2.s-2 (stored as ppm2)

The relax user manual (PDF), created 2016-10-28.