| Summary: | <p>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 1 order of magnitude. This is evaluated by simulating the time evolution of the nuclear
magnetization using a complete relaxation rate-matrix approach. The
calculations show that the Solomon dependence of the paramagnetic relaxation
rates on the metal–proton distance (as <span class="inline-formula"><i>r</i><sup>−6</sup></span>) can be incorrect for protons farther than 15 Å from the metal and thus can cause sizable errors in <span class="inline-formula"><i>R</i><sub>1</sub></span>-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 paramagnetic Solomon equation.
Therefore, it may contribute significantly to the water proton relaxation
rates measured at magnetic resonance imaging (MRI) magnetic fields in the presence of slow-rotating nanoparticles containing paramagnetic ions and a large number of
exchangeable surface protons.</p>
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