Implemented models

A number of analytic and numeric models are supported within relax. These cover single quantum (SQ) CPMG-type, combined proton-heteronuclear single quantum (SQ), zero quantum (ZQ), double quantum (DQ) and multi quantum (MQ) CPMG-type experiments, and R1ρ-type. If the model you are interested in is not available, please see Section 11.11 on page [*] for how you can add new models to relax.

Models which are independent of the experiment type include:

`R2eff':
This is the model used to determine the R2eff or R1ρ values and errors required as the base data for all other models. See Section 11.2.1 on page [*].
`No Rex':
This is the model for no chemical exchange being present. See Section 11.2.2 on page [*].

For the SQ CPMG-type experiments, the analytic models currently supported are:

`LM63':
The original Luz and Meiboom (1963) 2-site fast exchange equation with parameters {R20,..., Φex, kex}. See Section 11.3.1 on page [*].
`LM63 3-site':
The original Luz and Meiboom (1963) 3-site fast exchange equation with parameters {R20,..., Φex, B, kB, Φex, C, kC}. The equations of O'Connell et al. (2009) can be used to approximately convert the parameters {Φex, B, kB, Φex, C, kC} to more biologically relevant parameters. See Section 11.3.2 on page [*].
`CR72':
The reduced Carver and Richards (1972) 2-site equation for most time scales whereby the simplification R2A0 = R2B0 is assumed. It has the parameters {R20,..., pA, Δω, kex}. See Section 11.3.4 on page [*].
`CR72 full':
The full Carver and Richards (1972) 2-site equation for most time scales with parameters {R2A0, R2B0,..., pA, Δω, kex}. See Section 11.3.3 on page [*].
`IT99':
The Ishima and Torchia (1999) 2-site model for all time scales with pA $ \gg$ pB and with parameters {R20,..., pA, Δω, τex}. See Section 11.3.5 on page [*].
`TSMFK01':
The Tollinger et al. (2001) 2-site very-slow exchange model for time scales within range of microsecond to second time scale. Applicable in the limit of slow exchange, when | R2A0 - R2B0| $ \ll$ kAB, kBA $ \ll$ 1/τCPMG. 2*τCPMG is the time between successive 180 degree pulses. Parameters are {R2A0,..., Δω, kAB}. See Section 11.3.6 on page [*].
`B14':
The reduced Baldwin (2014) 2-site exact solution equation for all time scales whereby the simplification R2A0 = R2B0 is assumed. It has the parameters {R20,..., pA, Δω, kex}. See Section 11.3.8 on page [*].
`B14 full':
The full Baldwin (2014) 2-site exact equation for all time scales with parameters {R2A0, R2B0,..., pA, Δω, kex}. See Section 11.3.7 on page [*].

For the SQ CPMG-type experiments, the numeric models currently supported are:

`NS CPMG 2-site expanded':
A model for 2-site exchange expanded using Maple by Nikolai Skrynnikov (Tollinger et al., 2001). It has the parameters {R20,..., pA, Δω, kex}. See Section 11.4.1 on page [*].
`NS CPMG 2-site 3D':
The reduced model for 2-site exchange using 3D magnetisation vectors whereby the simplification R2A0 = R2B0 is assumed. It has the parameters {R20,..., pA, Δω, kex}. See Section 11.4.3 on page [*].
`NS CPMG 2-site 3D full':
The full model for 2-site exchange using 3D magnetisation vectors with parameters {R2A0, R2B0,..., pA, Δω, kex}. See Section 11.4.2 on page [*].
`NS CPMG 2-site star':
The reduced model for 2-site exchange using complex conjugate matrices whereby the simplification R2A0 = R2B0 is assumed. It has the parameters {R20,..., pA, Δω, kex}. See Section 11.4.5 on page [*].
`NS CPMG 2-site star full':
The full model for 2-site exchange using complex conjugate matrices with parameters {R2A0, R2B0,..., pA, Δω, kex}. See Section 11.4.4 on page [*].

For the combined proton-heteronuclear SQ, ZQ, DQ and MQ CPMG-type experiments (MMQ - or multi-multiple quantum), the analytic models currently supported are:

`MMQ CR72':
The Carver and Richards (1972) 2-site model for most time scales expanded for MMQ CPMG data by Korzhnev et al. (2004a). It has the parameters {R20,..., pA, Δω, ΔωH, kex}. See Section 11.5.1 on page [*].

For the combined proton-heteronuclear SQ, ZQ, DQ and MQ CPMG-type experiments (MMQ - or multi-multiple quantum), the numeric models currently supported are:

`NS MMQ 2-site':
The model for 2-site exchange whereby the simplification R2A0 = R2B0 is assumed. It has the parameters {R20,..., pA, Δω, ΔωH, kex}. See Section 11.6.1 on page [*].
`NS MMQ 3-site linear':
The model for 3-site exchange linearised with kAC = kCA = 0 whereby the simplification R2A0 = R2B0 = R2C0 is assumed. It has the parameters { R20, ..., pA, pB, ΔωAB, ΔωBC, ΔωHAB, ΔωHBC, kexAB, kexBC}. See Section 11.6.2 on page [*].
`NS MMQ 3-site':
The model for 3-site exchange whereby the simplification R2A0 = R2B0 = R2C0 is assumed. It has the parameters { R20, ..., pA, pB, ΔωAB, ΔωBC, ΔωHAB, ΔωHBC, kexAB, kexBC, kexAC}. See Section 11.6.3 on page [*].

For the R1ρ-type experiments, the analytic models currently supported are:

`M61':
The Meiboom (1961) 2-site fast exchange equation for on-resonance data with parameters {R1ρ',..., Φex, kex}. See Section 11.7.1 on page [*].
`DPL94':
The Davis et al. (1994) extension of the `M61' model for off-resonance data with parameters {R1ρ',..., Φex, kex}. See Section 11.7.3 on page [*].
`M61 skew':
The Meiboom (1961) 2-site equation for all time scales with pA $ \gg$ pB and with parameters {R1ρ',..., pA, Δω, kex}. This model is disabled by default in the dispersion auto-analysis. See Section 11.7.2 on page [*].
`TP02':
The Trott and Palmer (2002) 2-site equation for all time scales with pA $ \gg$ pB and with parameters {R1ρ',..., pA, Δω, kex}. See Section 11.7.4 on page [*].
`TAP03':
The Trott et al. (2003) off-resonance 2-site analytic equation for all time scales with the weak condition pA $ \gg$ pB and with parameters {R1ρ',..., pA, Δω, kex}.
`MP05':
The Miloushev and Palmer (2005) off-resonance 2-site equation for all time scales with parameters {R1ρ',..., pA, Δω, kex}. See Section 11.7.6 on page [*].

For the R1ρ-type experiments, the numeric models currently supported are:

`NS R1rho 2-site':
The model for 2-site exchange using 3D magnetisation vectors. It has the parameters {R1ρ',..., pA, Δω, kex}. See Section 11.8.1 on page [*].
`NS R1ρ 3-site linear':
The model for 3-site exchange linearised with kAC = kCA = 0 whereby the simplification R1ρA' = R1ρB' = R1ρC' is assumed. It has the parameters { R1ρ', ..., pA, pB, ΔωAB, ΔωBC, kexAB, kexBC}. See Section 11.8.3 on page [*].
`NS R1ρ 3-site':
The model for 3-site exchange whereby the simplification R1ρA' = R1ρB' = R1ρC' is assumed. It has the parameters { R1ρ', ..., pA, pB, ΔωAB, ΔωBC, kexAB, kexBC, kexAC}. See Section 11.8.2 on page [*].

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