NS R1rho 2-site
The relaxation dispersion model for the numeric solution (NS) to the Bloch-McConnell equations for 2-site exchange for R1rho-type data. This model is labelled as NS R1rho 2-site in relax.
Equation
This is the numerical model for 2-site exchange using 3D magnetisation vectors. It is selected by setting the model to NS R1rho 2-site. The simple constraint pA > pB is used to halve the optimisation space, as both sides of the limit are mirror image spaces.
For this model, the equations from Korzhnev05 have been used. The R1ρ value for state A magnetisation is defined as
[math] \begin{equation} \mathrm{R}_{1\rho} = - \frac{1}{T_\textrm{relax}} \cdot \ln \left( M_0^T \cdot e^{R \cdot T_\textrm{relax}} \cdot M_0 \right), \end{equation} [/math]
where
[math] \begin{align} M_0 &= \begin{pmatrix} \sin{\theta} \\ 0 \\ \cos{\theta} \\ 0 \\ 0 \\ 0 \end{pmatrix}, \\ \theta &= \arctan \left( \frac{\omega_1}{\Omega_\textrm{A}} \right). \end{align} [/math]
The relaxation evolution matrix is defined as
[math] \begin{equation} R = \begin{pmatrix} -\mathrm{R}_{1\rho}{´}-\textrm{k}_\textrm{AB} & -\delta_A & 0 & \textrm{k}_\textrm{BA} & 0 & 0 \\ \delta_A & -\mathrm{R}_{1\rho}{´}-\textrm{k}_\textrm{AB} & -\omega_1 & 0 & \textrm{k}_\textrm{BA} & 0 \\ 0 & \omega_1 & -\mathrm{R}_1-\textrm{k}_\textrm{AB} & 0 & 0 & \textrm{k}_\textrm{BA} \\ \textrm{k}_\textrm{AB} & 0 & 0 & -\mathrm{R}_{1\rho}{´}-\textrm{k}_\textrm{BA} & -\delta_B & 0 \\ 0 & \textrm{k}_\textrm{AB} & 0 & \delta_B & -\mathrm{R}_{1\rho}{´}-\textrm{k}_\textrm{BA} & -\omega_1 \\ 0 & 0 & \textrm{k}_\textrm{AB} & 0 & \omega_1 & -\mathrm{R}_1-\textrm{k}_\textrm{BA} \\ \end{pmatrix}, \end{equation} [/math]
Essentials
It is essential to read in R1 values before starting a calculation:
relax_data.read(ri_id='R1', ri_type='R1', frq=cdp.spectrometer_frq_list[0], file='R1_values.txt', mol_name_col=1, res_num_col=2, res_name_col=3, spin_num_col=4, spin_name_col=5, data_col=6, error_col=7)
Where the data could be stored like
# mol_name res_num res_name spin_num spin_name value error
None 13 L None N 1.323940 0.146870
None 15 R None N 1.344280 0.140560
None 16 T None N 1.715140 0.136510
Parameters
The NS R1rho 2-site model has the parameters {R1ρ', ..., pA, Δω, kex}.
Reference
The reference for the NS R1rho 2-site model is:
- Korzhnev, D. M., Orekhov, V. Y., and Kay, L. E. (2005). Off-resonance R(1rho) NMR studies of exchange dynamics in proteins with low spin-lock fields: an application to a Fyn SH3 domain. J. Am. Chem. Soc., 127(2), 713-721. (DOI: 10.1021/ja0446855)
Links
The implementation of the NS R1rho 2-site model in relax can be seen in the:
