Revisiting paramagnetic relaxation enhancements in slowly rotating systems: how long is the long range?

Cross relaxation terms in paramagnetic systems that reorient rigidly with slow tumbling times can increase the effective longitudinal relaxation rates of protons of more than one order of magnitude. This is evaluated by simulating the time evolution of the nuclear magnetization using a complete relaxation matrix approach. The calculations show that the Solomon dependence of the relaxation rates on the metal-proton distance (as r−6) can be incorrect for protons farther than 15 Å from the metal, and thus can originate sizable errors in R1-derived distance restraints used, for instance, for protein structure determination. Furthermore, the chemical exchange of these protons with bulk water protons can enhance the relaxation rate of the solvent protons by far more than expected from the Solomon equation. Therefore, it may contribute significantly to the water proton relaxation rates measured at MRI magnetic fields in the presence of slow-rotating nanoparticles containing paramagnetic ions and a large number of exchangeable surface protons.