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 R_1ρ-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 R_2eff or R_1ρ 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,..., Φ_ex, k_ex}. See Section 11.3.1 on page .

`LM63 3-site':

The original Luz and Meiboom (1963) 3-site fast exchange equation with parameters {R₂⁰,..., Φ_{ex, B}, k_B, Φ_{ex, C}, k_C}. The equations of O'Connell et al. (2009) can be used to approximately convert the parameters {Φ_{ex, B}, k_B, Φ_{ex, C}, k_C} 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 R_2A⁰ = R_2B⁰ is assumed. It has the parameters {R₂⁰,..., p_A, Δω, k_ex}. See Section 11.3.4 on page .

`CR72 full':

The full Carver and Richards (1972) 2-site equation for most time scales with parameters {R_2A⁰, R_2B⁰,..., p_A, Δω, k_ex}. See Section 11.3.3 on page .

`IT99':

The Ishima and Torchia (1999) 2-site model for all time scales with p_A $\gg$ p_B and with parameters {R₂⁰,..., p_A, Δω, τ_ex}. 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 | R_2A⁰ - R_2B⁰| $\ll$ k_AB, k_BA $\ll$ 1/τ_CPMG. 2*τ_CPMG is the time between successive 180 degree pulses. Parameters are {R_2A⁰,..., Δω, k_AB}. See Section 11.3.6 on page .

`B14':

The reduced Baldwin (2014) 2-site exact solution equation for all time scales whereby the simplification R_2A⁰ = R_2B⁰ is assumed. It has the parameters {R₂⁰,..., p_A, Δω, k_ex}. See Section 11.3.8 on page .

`B14 full':

The full Baldwin (2014) 2-site exact equation for all time scales with parameters {R_2A⁰, R_2B⁰,..., p_A, Δω, k_ex}. 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,..., p_A, Δω, k_ex}. 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 R_2A⁰ = R_2B⁰ is assumed. It has the parameters {R₂⁰,..., p_A, Δω, k_ex}. 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 {R_2A⁰, R_2B⁰,..., p_A, Δω, k_ex}. 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 R_2A⁰ = R_2B⁰ is assumed. It has the parameters {R₂⁰,..., p_A, Δω, k_ex}. 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 {R_2A⁰, R_2B⁰,..., p_A, Δω, k_ex}. 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,..., p_A, Δω, Δω^H, k_ex}. 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 R_2A⁰ = R_2B⁰ is assumed. It has the parameters {R₂⁰,..., p_A, Δω, Δω^H, k_ex}. See Section 11.6.1 on page .

`NS MMQ 3-site linear':

The model for 3-site exchange linearised with k_AC = k_CA = 0 whereby the simplification R_2A⁰ = R_2B⁰ = R_2C⁰ is assumed. It has the parameters { R₂⁰, ..., p_A, p_B, Δω_AB, Δω_BC, Δω^H_AB, Δω^H_BC, k_ex^AB, k_ex^BC}. See Section 11.6.2 on page .

`NS MMQ 3-site':

The model for 3-site exchange whereby the simplification R_2A⁰ = R_2B⁰ = R_2C⁰ is assumed. It has the parameters { R₂⁰, ..., p_A, p_B, Δω_AB, Δω_BC, Δω^H_AB, Δω^H_BC, k_ex^AB, k_ex^BC, k_ex^AC}. See Section 11.6.3 on page .

For the R_1ρ-type experiments, the analytic models currently supported are:

`M61':

The Meiboom (1961) 2-site fast exchange equation for on-resonance data with parameters {R_1ρ',..., Φ_ex, k_ex}. See Section 11.7.1 on page .

`DPL94':

The Davis et al. (1994) extension of the `M61' model for off-resonance data with parameters {R_1ρ',..., Φ_ex, k_ex}. See Section 11.7.3 on page .

`M61 skew':

The Meiboom (1961) 2-site equation for all time scales with p_A $\gg$ p_B and with parameters {R_1ρ',..., p_A, Δω, k_ex}. 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 p_A $\gg$ p_B and with parameters {R_1ρ',..., p_A, Δω, k_ex}. 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 p_A $\gg$ p_B and with parameters {R_1ρ',..., p_A, Δω, k_ex}.

`MP05':

The Miloushev and Palmer (2005) off-resonance 2-site equation for all time scales with parameters {R_1ρ',..., p_A, Δω, k_ex}. See Section 11.7.6 on page .

For the R_1ρ-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 {R_1ρ',..., p_A, Δω, k_ex}. See Section 11.8.1 on page .

`NS R_1ρ 3-site linear':

The model for 3-site exchange linearised with k_AC = k_CA = 0 whereby the simplification R_1ρA' = R_1ρB' = R_1ρC' is assumed. It has the parameters { R_1ρ', ..., p_A, p_B, Δω_AB, Δω_BC, k_ex^AB, k_ex^BC}. See Section 11.8.3 on page .

`NS R_1ρ 3-site':

The model for 3-site exchange whereby the simplification R_1ρA' = R_1ρB' = R_1ρC' is assumed. It has the parameters { R_1ρ', ..., p_A, p_B, Δω_AB, Δω_BC, k_ex^AB, k_ex^BC, k_ex^AC}. See Section 11.8.2 on page .