Paramagnetic Relaxation Enhancement Restraints

Paramagnetic relaxation enhancement can be used to derive a distance estimate. The transverse relaxation rate is given by the Solomon-Bloembergen equation:

$$\Gamma_2=r_{AB}^{-6} C_{AB} \left( 4\tau_c +\frac{3\tau_c}{1+(\omega_I\tau_c)^2}\right),$$ (34.1)

where $r_{AB}$ is the distance between a proton and the paramagnetic center, $C_{AB}$ is a collection of constants (depending on atom types), $\tau_c$ is the correlation time and $\omega_I$ is the proton's Larmor frequency.

The energy term takes the form

$$E_{PMAG}=K_{PMAG} (\Gamma_2^{calc}-\Gamma_2^{obs})^2 \left[... ...amma_2^{obs}}{\sqrt{2}\sigma_\Gamma}\right)^2\right] \right],$$ (34.2)

where $\sigma_\Gamma$ is the estimated uncertainty in the measured values of $\Gamma$.

See Donaldson et al. (2001) for more information.