High Relaxivity with No Coordinated Waters: A Seemingly Paradoxical Behavior of [Gd(DOTP)]5– Embedded in Nanogels

Nanogels (NGs) obtained by electrostatic interactions between chitosan and hyaluronic acid and comprising paramagnetic Gd chelates are gaining increasing attention for their potential application in magnetic resonance bioimaging. Herein, the macrocyclic complexes [Gd(DOTP)]5−, lacking metal-bound water molecules (q = 0), were confined or used as a cross-linker in this type of NG. Unlike the typical behavior of Gd complexes with q = 0, a remarkable relaxivity value of 78.0 mM–1 s–1 was measured at 20 MHz and 298 K, nearly 20 times greater than that found for the free complex. A careful analysis of the relaxation data emphasizes the fundamental role of second sphere water molecules with strong and long-lived hydrogen bonding interactions with the complex. Finally, PEGylated derivatives of nanoparticles were used for the first in vivo magnetic resonance imaging study of this type of NG, revealing a fast renal excretion of paramagnetic complexes after their release from the NGs.


Field dependence of water proton relaxivity
The difference in the longitudinal relaxation rates of solvent ligand nuclei between a paramagnetic solution and a diamagnetic reference solution is where R1M is the relaxation rate of the ligand nuclei bound to the paramagnetic metal ion, M is their exchange time, fM is the mole fraction of ligand nuclei bound to the metal and 1OS is the outersphere relaxation rate. The relaxivity r1 is defined as the paramagnetic enhancement of the solvent nuclear relaxation rates in the presence of 0.001 mol/dm 3 of paramagnetic metal ions in solution.
Therefore, the relaxivity in a water solution is where q is the number of water molecules coordinated to each paramagnetic metal ion and 1OS is equal to 1OS divided by the millimolar concentration of the paramagnetic metal ion. When M < 1 −1 , the coordinated water molecule(s) are in the so-called fast exchange.
The paramagnetic relaxation rate R1M due to the point dipole-point dipole interaction between the water proton magnetic moment and the unpaired electron(s) magnetic moment is described by the Solomon equation where 0 is the permeability of the vacuum, is the proton magnetogyric ratio, is the electron Bohr magneton, S is the electron spin quantum number, r is the distance between paramagnetic metal and proton of the coordinated water molecule, and are the electron and proton Larmor frequency, respectively, and the correlation time is given by The electron relation rate 1 is described by the Bloembergen-Morgan equation (pseudorotation model) where Δ 2 is the mean squared fluctuation of the zero-field splitting (ZFS), called squared transient ZFS, and is the correlation time for the instantaneous distortions of the metal coordination polyhedron.
Besides the overall molecular reorientation, occurring with correlation time R , faster internal motions, with correlation time f , can also modulate (at least partially) the electron-nucleus dipoledipole interaction. In the Lipari-Szabo model-free treatment, Eq.
(3) should thus be replaced by The outer-sphere relaxivity is due to the water molecules diffusing around the paramagnetic metal ion, and, assuming that metal and ligand nuclei are in the center of hard sphere spherical molecules, according to one of the most commonly used models for diffusion where A is the Avogadro constant, a is the distance of closest approach between the ligand nuclei and = 2 (10)

Zero-field splitting effects
Eqs. 3 and 6 are derived in the absence of static ZFS. In the presence of ZFS, the energies of the electron spin states can be very different from what predicted from the Zeeman term. These differences affect the transition probabilities between the different states, and thus the nuclear relaxivity. The extent of this effect largely depends on the magnitude of the static ZFS and on the position of the nucleus with respect to the z axis of the ZFS tensor. In the so-called slow rotation limit ( ≫ 1 −1 ) and within the Redfield limit, the modified Florence NMRD program was used to calculate the relaxivity profiles as a function of these parameters (static ZFS and angle between the z axis of the ZFS tensor and the metal-water protons direction).
The effects of static ZFS on the relaxivity profiles become negligible at electron Larmor frequencies larger than the ZFS frequency (equal to ZFS in cm −1 times 2c, where c is the velocity of light). For Gd 3+ complexes, where ZFS is smaller than 0.05 cm −1 , this corresponds to proton Larmor frequencies larger than ca. 10 MHz.

In vitro stability tests
In vitro stability tests were carried out on PEGylated nanogels in human serum (Seronorm™) at pH=7. To this purpose, the NG-2-PEG were diluted in human serum (Gd(III) concentration: 0.159 mM) and subjected to continuous gentle vortexing at 37°C. The R1 was measured at 21.5 MHz and 25 °C at different time points, starting from time 0 to 170 hours post incubation ( Figure S10).
To investigate the potential release of the complex from the NG-2-PEG, two dialysis cycles ( Table S1. Parameters from the analysis of 1 H NMRD data.