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\caption[The parameters of relaxation dispersion.]{The parameters of relaxation dispersion.}

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Parameter          & Equation                       & Description                                                                   & Units \\
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\label{table: dispersion parameters}

$\nucpmg$          & $1 / (4 \taucpmg)$             & CPMG frequency                                                                & Hz \\
$\taucpmg$         & $1 / (4 \nucpmg)$              & Delay between CPMG $\pi$ pulses                                               & s \\
$T_\textrm{relax}$ & -                              & The relaxation delay period                                                   & s \\
$I_0$              & -                              & Reference peak intensity when $T_\textrm{relax}$ is zero                      & - \\
$I_1$              & -                              & Peak intensity for a given $\nucpmg$ or spin-lock field strength $\omega_1$   & - \\
$\Rtwozero$        & -                              & $\Rtwo$ relaxation rate in the absence of exchange                            & rad.s$^{-1}$ \\
$\RtwozeroA$       & -                              & $\Rtwo$ relaxation rate for state A in the absence of exchange                & rad.s$^{-1}$ \\
$\RtwozeroB$       & -                              & $\Rtwo$ relaxation rate for state B in the absence of exchange                & rad.s$^{-1}$ \\
$\Ronerhoprime$    & -                              & $\Ronerho$ relaxation rate in the absence of exchange                         & rad.s$^{-1}$ \\
$\aveoffset$       & $\aveomega - \omegarf$         & The average resonance offset in the rotating frame                            & rad.s$^{-1}$ \\
$\offsetA$         & $\omegaA - \omegarf$           & The resonance offset in the rotating frame for state A                        & rad.s$^{-1}$ \\
$\offsetB$         & $\omegaB - \omegarf$           & The resonance offset in the rotating frame for state B                        & rad.s$^{-1}$ \\
$\offsetC$         & $\omegaC - \omegarf$           & The resonance offset in the rotating frame for state C                        & rad.s$^{-1}$ \\
$\omegaA$          & -                              & The Larmor frequency of the spin in state A                                   & rad.s$^{-1}$ \\
$\omegaB$          & -                              & The Larmor frequency of the spin in state B                                   & rad.s$^{-1}$ \\
$\omegaC$          & -                              & The Larmor frequency of the spin in state C                                   & rad.s$^{-1}$ \\
$\omegaHA$         & -                              & The proton Larmor frequency of the spin in state A (for MMQ data)             & rad.s$^{-1}$ \\
$\omegaHB$         & -                              & The proton Larmor frequency of the spin in state B (for MMQ data)             & rad.s$^{-1}$ \\
$\omegaHC$         & -                              & The proton Larmor frequency of the spin in state C (for MMQ data)             & rad.s$^{-1}$ \\
$\aveomega$        & $\pA\omegaA + \pB\omegaB$      & The population averaged Larmor frequency of the spin                          & rad.s$^{-1}$ \\
$\omegaone$        & -                              & Spin-lock field strength, i.e.\ the amplitude of the rf field                 & rad.s$^{-1}$ \\
$\omegae$          & $\sqrt{\aveoffset^2 + \omegaone^2}$  & Effective field in the rotating frame                                   & rad.s$^{-1}$ \\
$\omegarf$         & -                              & Spin-lock offset, i.e.\ the frequency of the rf field                         & rad.s$^{-1}$ \\
$\theta$           & $\arctan \left( \frac{\omegaone}{\aveoffset} \right)$  & Rotating frame tilt angle                             & rad \\
$\kAB$             & $\pB\kex$                      & The forward exchange rate from state A to state B (2-site)                    & rad.s$^{-1}$ \\
$\kBA$             & $\pA\kex$                      & The reverse exchange rate from state B to state A (2-site)                    & rad.s$^{-1}$ \\
$\kAB$             & $\pB\kexAB$                    & The forward exchange rate from state A to state B (3-site)                    & rad.s$^{-1}$ \\
$\kBA$             & $\pA\kexAB$                    & The reverse exchange rate from state B to state A (3-site)                    & rad.s$^{-1}$ \\
$\kBC$             & $\pC\kexBC$                    & The forward exchange rate from state B to state C (3-site)                    & rad.s$^{-1}$ \\
$\kCB$             & $\pB\kexBC$                    & The reverse exchange rate from state C to state B (3-site)                    & rad.s$^{-1}$ \\
$\kAC$             & $\pC\kexAC$                    & The forward exchange rate from state A to state C (3-site)                    & rad.s$^{-1}$ \\
$\kCA$             & $\pA\kexAC$                    & The reverse exchange rate from state C to state A (3-site)                    & rad.s$^{-1}$ \\
$\kex$             & $1 / \tex$                     & 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$^{-1}$ \\
$\tex$             & $1 / \kex$                     & 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)                                                & - \\
$\dw$              & $\omegaB-\omegaA$              & Chemical shift difference between sites A and B (2-site)                      & rad.s$^{-1}$ (stored as ppm) \\
$\dwAB$            & $\omegaB-\omegaA$              & Chemical shift difference between sites A and B (3-site)                      & rad.s$^{-1}$ (stored as ppm) \\
$\dwBC$            & $\omegaC-\omegaB$              & Chemical shift difference between sites B and C (3-site)                      & rad.s$^{-1}$ (stored as ppm) \\
$\dwAC$            & $\dwAB+\dwBC$                  & Chemical shift difference between sites A and C (3-site)                      & rad.s$^{-1}$ (stored as ppm) \\
$\dwH$             & $\omegaHB-\omegaHA$            & Proton chemical shift difference between sites A and B (2-site)               & rad.s$^{-1}$ (stored as ppm) \\
$\dwHAB$           & $\omegaHB-\omegaHA$            & Proton chemical shift difference between sites A and B (3-site)               & rad.s$^{-1}$ (stored as ppm) \\
$\dwHBC$           & $\omegaHC-\omegaHB$            & Proton chemical shift difference between sites B and C (3-site)               & rad.s$^{-1}$ (stored as ppm) \\
$\dwHAC$           & $\dwHAB+\dwHBC$                & Proton chemical shift difference between sites A and C (3-site)               & rad.s$^{-1}$ (stored as ppm) \\
$\Phiex$           & $\pA\pB\dw^2$                  & Fast exchange factor                                                          & rad$^2$.s$^{-2}$ (stored as ppm$^2$) \\
$\PhiexB$          & See \ref{eq: disp phiexB} on page \pageref{eq: disp phiexB} & Fast exchange factor between sites A and B       & rad$^2$.s$^{-2}$ (stored as ppm$^2$) \\
$\PhiexC$          & See \ref{eq: disp phiexC} on page \pageref{eq: disp phiexC} & Fast exchange factor between sites A and C       & rad$^2$.s$^{-2}$ (stored as ppm$^2$) \\

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