Abstract
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 ) can be incorrect for protons farther than 15 Å from the metal and thus can cause sizable errors in -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.
Highlights
Paramagnetic relaxation rates are largely applied for macromolecular structure determination, because they provide information on the distance of the macromolecule nuclei from the paramagnetic metal ion as well as in the field of magnetic resonance imaging (MRI) (Bertini et al, 2017)
We explore the possibility of increasing the efficacy of a paramagnetic molecule as an MRI contrast agent by exploiting cross-relaxation effects
The relaxation rates of all protons belonging to a macromolecule containing a paramagnetic metal ion can be calculated using a modified version of program CORMA (Borgias et al, 1989), called CORMA-PODS (COmplete Relaxation Matrix Analysis – Paramagnetic Or Diamagnetic Solutions)
Summary
Paramagnetic relaxation rates are largely applied for macromolecular structure determination, because they provide information on the distance of the macromolecule nuclei from the paramagnetic metal ion as well as in the field of magnetic resonance imaging (MRI) (Bertini et al, 2017). We have here modified program CORMA to calculate (i) the longitudinal relaxation rates of protons in molecules with known structure, in the presence of paramagnetic ions, taking into account all cross-relaxation effects, and (ii) the longitudinal relaxation rates of the bulk water protons, in the presence of some protons of the molecule in exchange with the bulk (Libralesso et al, 2005; Ravera et al, 2013) This model allowed us to calculate the deviations of the relaxation enhancements with respect to the values predicted by the paramagnetic Solomon equation on the basis of the metal–proton distances and the gain in relaxation rate values due to the network of the dipole–dipole interactions
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