Predicting the Thermodynamic Stability of Zirconium Radiotracers

The thermodynamic stability of a metal−ligand complex, as measured by the formation constant (logβ), is one of themost important parameters that determines metal ion selectivity and potential applications in, for example, radiopharmaceuticalscience. The stable coordination chemistry of radioactive89Zr4+in an aqueous environment is of paramount importance whendeveloping 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 of89Zr-labeled proteins, but the coordination ofDFO to Zr4+ions is suboptimal. Many alternative ligands have been reported, but the challenges in measuring very high logβvalueswith metal ions such as Zr4+that tend to hydrolyze mean that accurate thermodynamic data are scarce. In this work, densityfunctional theory (DFT) calculations were used to predict the reaction energetics for metal ion complexation. Computed values ofpseudoformation constants (logβ′) 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 17different ligands, including many of the alternative bifunctional chelates that have been reported recently for use in89Zr4+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 offuture ligands. The computational model developed here is straightforward and reproducible and can be readily applied in the designof other metal coordination compounds