MD Simulations of Acyclic and Macrocyclic Gd3+‐Based MRI Contrast Agents: Influence of the Internal Mobility on Water Proton Relaxivity

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Abstract
Classical molecular dynamics simulations with a force field adapted to the family of Gd3+ polyaminocarboxylate complexes have been successfully applied on two macrocyclic ([Gd(DOTA)(H2O)]− and [Gd(DO3A)(H2O)2]) and two acyclic ([Gd(DTPA)(H2O)]2− and [Gd(EGTA)(H2O)]−) complexes in aqueous solution (DOTA=1,4,7,10-tetrakis(carboxymethyl)-1,4,7,10-tetraazacyclododecane, DO3A=1,4,6-tris(carboxymethyl)-1,4,7,10-tetraazacyclododecane, DTPA=1,1,4,7,7-pentakis(carboxymethyl)-1,4,7-triazaheptane, EGTA=1,1,10,10-tetrakis(carboxymethyl)-1,10-diaza-4,7-dioxadecane). In both macrocylic complexes the Gd3+ coordination polyhedron remains close to a monocapped square antiprism (MSA) during the entire simulation time. For the stereolabile acyclic complexes different interconverting sets of geometries are observed: three sets close to tricapped trigonal prisms (TTP) for [Gd(EGTA)(H2O)]− and three sets intermediate between MSA and TTP (distorted C2v symmetry) for [Gd(DTPA)(H2O)]2−. The fast conformational changes observed in the acyclic complexes might weaken the hydration of the second water shell and therefore disfavour the outer-sphere relaxivity. Moreover, the motions of the chelate observed in both acyclic complexes involve the reorientation of the symmetry elements over time. This reorientation, occurring on a picosecond timescale, can be associated with the correlation time for modulation of the zero field splitting and might participate in the electron spin relaxation mechanisms of the Gd3+ ion. The internal motion of the inner-sphere water molecule can be quantified by the ratio τR(GDHW)/τR(GDOW) which increases slightly from 0.7 for the acyclic to 0.8 for the macrocyclic complexes. This increase for the macrocylic chelates is favourable for a higher relaxivity and can be related to their rigidity. The water exchange rate on the four complexes has been related to the steric constraint of the ligand on the inner-sphere water molecule(s), which is inversely proportional to a geometrical descriptor, the solid angle ψ. A range of ψ values is given (2≪ψ<3.3) where the exchange should be optimal. The observations made on the picosecond timescale give general directions for the design of more efficient magnetic resonance imaging contrast agents.

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