Model-free nuclear magnetic resonance study of intermolecular free energy landscapes in liquids with paramagnetic Ln3+ spotlights: Theory and application to Arg-Gly-Asp

Abstract

We propose an easily applicable method for investigating the pair distribution function of a lanthanide Ln(3+) complex LnL (L = ligand) with respect to any solvent or solute molecule A carrying observable nuclear spins. Let r be the distance of Ln(3+) to the observed nuclear spin I. We derive a simple expression of the experimental value of the configurational average of 1/r(6) in terms of longitudinal paramagnetic relaxation (rate) enhancements (PREs) of the spin I measured on a standard high-resolution NMR spectrometer and due to well-chosen concentrations of LnL complexes in which Ln(3+) is a fast-relaxing paramagnetic lanthanide or the slowly-relaxing gadolinium Gd(3+). The derivation is justified in the general case of a molecule A which is by turns in a bound state where it follows the complex and a free state where it moves independently. It rests on the expression of the underlying PRE theory in terms of the angle-dependent pair distribution function of LnL and A. The simplifications of this theory in the high-field regime and under the condition of fast exchange between bound and free states are carefully discussed. We also show that original information on the angle dependence of the molecular pair distribution function can be gained from the measured paramagnetic dipolar shifts induced by complexed fast-relaxing Ln(3+) ions. The method is illustrated by the case study of the anionic Lnttha(3-) = [Ln(3+)(ttha)](3-) (ttha(6-) = triethylene tetraamine hexacetate) complex interacting with the biologically important tripeptide Arg-Gly-Asp (RGD) which carries peripheral ionic groups. The usefulness of an auxiliary reference outer sphere probe solute is emphasized.