Relaxivity second-sphere contribution

The smaller contribution to solvent proton relaxation due to the slow exchanging regime also allows detection of second and outer sphere contributions (62). In fact outer-sphere and/or second sphere protons contribute less than 5% of proton relaxivity for the highest temperature profile, and to about 30% for the lowest temperature profile. The fact that they affect differently the profiles acquired at different temperature influences the best-fit values of all parameters with respect to the values obtained without including outer and second sphere contributions, and not only the value of the first sphere proton-metal ion distance (as it usually happens for the other metal aqua ions). A simultaneous fit of longitudinal and transverse relaxation rates provides the values of the distance of the 12 water protons from the metal ion (2.71 A), of the transient ZFS (0.11 cm ), of the correlation time for electron relaxation (about 2 x 10 s at room temperature), of the reorienta-tional time (about 70 x 10 s at room temperature), of the lifetime (about 7 x 10 s at room temperature), of the constant of contact interaction (2.1 MHz). A second coordination sphere was considered with 26 fast exchanging water protons at 4.5 A from the metal ion (99), and the distance of closest approach was fixed in the range between 5.5 and 6.5 A. 

Both the inner- and the second-sphere contributions to the overall relaxivity are directly dependent on the molar fraction of water protons interacting with the paramagnetic center (see Eq. (3)). Therefore, a relaxivity enhancement might be simply obtained by increasing the number of water protons in the coordination shells (inner- and second-) of the Gd(III) ion. 

The picture is much more complicated in the presence of slow-exchanging protons with different lifetimes (see Section II.A.3). In the hypothesis that the closest protons are exchanging with a very low rate, for instance, and second sphere water protons are fast-exchanging, the latter will provide the largest contribution to relaxation (for an example see. Section II. C). 

DTPA and all DTPA-bisamides reported up to now bind Ln3+ ions in a 8-coordi-nate fashion through the three N atoms of the diethylenetriamine backbone and five carboxylate and/or amide O-atoms, both in the solid and in solution. An inspection of crystal structures shows that diethylenetriamine moieties in these complexes always occur either in the XX or in the 88 conformation [ 1,2]. In these conformations, steric interactions are minimized. The coordination sphere is completed by one water molecule or, in some crystal structures, by the O-atom of a neighboring carboxylate group. In a recently reported low temperature (173 K) X-ray structure of K2 [Yb(DTPA)(H20)] second sphere waters were observed adjacent to the carboxylate oxygens [3]. The inner-sphere water is the most important source of the relaxivity of the corresponding Gd3+ complex, but the second sphere water molecules contribute significantly to it as well [3]. 

Another disadvantage of the small, hydrophilic agents is that they tumble very rapidly in the extracellular fluid. In water at 25 °C, for example, Gd-DTPA has a rotational correlation time (rR) of 58 ps as determined by the fitting of NMRD data [3], and 105 ps by EPR simulation in the VO++-DTPA analog [4]. This very rapid motion dominates the relaxivity of the PCA in the frequency range of typical clinical interest (42-63 MHz). The reasons for this dominance of rR can be traced to the fact that small Gd3+ chelates like Gd-DTPA have a relaxivity at clinical frequencies that is determined predominantly by an inner sphere process for Gd-DTPA at 50 MHz, Chen et al. calculate that the relaxivity in water is 43 % inner sphere, 25 % second sphere, and 32 % outer sphere [4]. In turn, the inner sphere contribution to relaxivity is often modeled by the Solomon-Bloem-bergen equations [5,6]... 

More precisely, the paramagnetic contribution of the longitudinal relaxation rate is composed of the inner-sphere relaxation, the second-sphere relaxation, and the outer-sphere relaxation. The model used to describe these interactions is shown in Figure 10.4. The various parameters that influence the observed longitudinal relaxivity will be discussed using Gd-based CAs as illustrative examples. 

More recent NMR studies have questioned the concept of outer sphere coordination of substrate. Andersson et al. have suggested that the magnetic relaxation rate of solvent protons in solutions of LADH with Co" ions substituted specifeally for zinc at the catalytic site arises mainly from diamagnetic contributions, and the paramagnetic contributions are relatively small.This puts into doubt the conclusions of Sloan et al. and Drysdale and Hollis, who assumed paramagnetic contributions were predominant their results suggesting second sphere coordination of substrate may require some reinterpretation. N NMR has also been informative in this system. 

Exciplexes and Second Sphere Interactions The concept of exdplex formation in inorganic systems has received considerable attention in recent years. Exciplexes can be observed when ground state complex formation is forbidden but the excited state complex has a shallow energy minimum that can radiatively decay to the ground state (Equation (6) and (7)). McMillin and co-workers postulated exdplex contributions to nonradiative relaxation of Cu phenanthroline... 

The second contribution to paramagnetic relaxation is the outer-sphere relaxation. It is explained by dipolar interactions at longer distances between the spins of the paramagnetic center and the nuclear spin. This intermolecular mechanism is modulated by the translational correlation time Tp, which takes into account the relative diffusion constant (D) of the Gd center and of the solvent molecule and their distance of closest approach (d). The outer-sphere contribution has been described by Freed and is given by equations (10) and (11) ... 

For Gd(III) complexes there are several processes that can contribute to this correlation time. Electronic relaxation (l/Fi e) at the Gd(III) ion, rotational diffusion (1/tr) of the complex, and water exchange in and out of die first (l/tn,) or 2nd (1/Xni ) coordination sphere all create a fluctuating field that can serve to relax the hydrogen nucleus. It is die fastest rate (shortest time constant) that determines the extent of relaxation. For water in the second sphere, the relevant correlation time may be the lifetime of diis water, which may be on the order of tens of picoseconds. Water in the inner sphere typically has a much longer residency time (1-10,000 ns), so the relevant correlation time is usually rotational diffusion or electronic relaxation. 

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