Predicting the Thermodynamic Stability of Zirconium Radiotracers

The thermodynamic stability of a metal-ligand complex, as measured by the formation constant (log β), is one of the most important parameters that determines metal ion selectivity and potential applications in, for example, radiopharmaceutical science. The stable coordination chemistry of radioactive ⁸⁹Zr⁴⁺ in an aqueous environment is of paramount importance when developing positron-emitting radiotracers based on proteins (usually antibodies) for use with positron emission tomography. Desferrioxamine B (DFO) remains the chelate of choice for clinical applications of ⁸⁹Zr-labeled proteins, but the coordination of DFO to Zr⁴⁺ ions is suboptimal. Many alternative ligands have been reported, but the challenges in measuring very high log β values with metal ions such as Zr⁴⁺ that tend to hydrolyze mean that accurate thermodynamic data are scarce. In this work, density functional theory (DFT) calculations were used to predict the reaction energetics for metal ion complexation. Computed values of pseudoformation constants (log β') are correlated with experimental data and showed an excellent linear relationship (R² = 0.97). The model was then used to estimate the absolute and relative formation constants of 23 different Zr⁴⁺ complexes using a total of 17 different ligands, including many of the alternative bifunctional chelates that have been reported recently for use in ⁸⁹Zr⁴⁺ radiochemistry. In addition, detailed computational studies were performed on the geometric isomerism and hydration state of Zr-desferrioxamine. Collectively, the results offer new insights into Zr⁴⁺ coordination chemistry that will help guide the synthesis of future ligands. The computational model developed here is straightforward and reproducible and can be readily applied in the design of other metal coordination compounds.