The NS MMQ 3-site model

This is the numerical model for 3-site exchange for proton-heteronuclear SQ, ZQ, DQ and MQ CPMG data, as derived in (Korzhnev et al., 2004a,b,2005a). However it has been extended to allow the AC transition. To simplify the optimisation space for the model as in the `NS MMQ 3-site linear' model, the assumption R2A0 = R2B0 = R2C0 = R20 has been made.

The SQ, ZD and DQ equations

The basic evolution matrices for single, zero and double quantum CPMG-type data for this model are

A± = ea±τCPMG, (11.70)


a± = $\displaystyle \begin{pmatrix}-\textrm{k}_{\textrm{AB}}-\textrm{k}_{\textrm{AC}}...
...{CB}}-\textrm{k}_{\textrm{CA}}\pm\imath\Delta\omega_{\textrm{AC}} \end{pmatrix}$    
           - $\displaystyle \begin{pmatrix}\mathrm{R}_{\mathrm{2A}}^0& 0 & 0 \\ 0 & \mathrm{R}_{\mathrm{2B}}^0& 0 \\ 0 & 0 & \mathrm{R}_{\mathrm{2C}}^0 \end{pmatrix}$. (11.71)

The MQ equations

The mj matrices for this model are

\begin{subequations}\begin{align}\mathbf{m_1} &= \begin{pmatrix}-\textrm{k}_{\te...
... 0 & 0 & \mathrm{R}_{\mathrm{2C}}^0 \end{pmatrix}. \end{align}\end{subequations}

More information about the NS MMQ 3-site model is available from:

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