Outer-Sphere Investigation of MRI Relaxation Contrast Agents. Example of a Cyclodecapeptide Gadolinium Complex with Second-Sphere Water

We show how the purely outer-sphere (OS) relaxivity of a probe solute due to a Gd3+ complex can help characterize the outer (0), inner (I), and second (2) sphere (S) contributions to the water proton relaxivity. Because of the difficulties of accurate theoretical predictions, we propose an experimental determination of the OS dipolar time correlation function (OS-DTCF) of the relative position of Gd3+ with respect to any of the equivalent protons of the purely OS probe p-dioxane, which moves around the complex without binding to it. The method is illustrated by the GdPA complex with PA = c(AspArgGluProGlyGluTrpAspProGly). The experimental DTCF for dioxane is obtained by a model-free analysis of the high-field relaxivity of its protons. The time-modulation of the dioxane DTCF by the Gd3+ electronic spin relaxation yields a measurable quenching of the longitudinal relaxivity at low-to-medium field, which serves us to deduce the fluctuating zero-field splitting (ZFS) Hamiltonian causing this electronic relaxation. The DTCF for water is derived from that for dioxane by appropriate scaling of the geometry of collision and relative diffusion coefficients of these molecules with respect to GdPA. The information obtained on the OS motion for water and the ZFS Hamiltonian together with an independent characterization of the IS contribution allows us to disentangle the OS, IS, and 2S mechanisms and interpret the relaxivity profile of the water protons from 2.35 mT to 18.8 T. The presence of a large 2S contribution is confirmed.