Predicting Reduction Potentials of Blue Copper Proteins Using Quantum Mechanical Calculations

We have calculated redox potentials of 12 blue copper protein sites comparing 64 computational methods, systematically varying the quantum mechanics (QM) system size, dielectric constants, density functional, and basis sets. All methods were based on structures optimized with combined QM and molecular mechanics (QM/MM) approaches. The redox potentials were evaluated using 10 quality metrics. The best results for relative potentials were achieved using a QM system of intermediate size (∼70 atoms), the TPSS density functional, and a SV(P) basis set, using QM-cluster calculations in a continuum solvent with a dielectric constant of 20, yielding a mean absolute deviation of 0.09 V and a maximum deviation of 0.26 V. For absolute redox potentials, methods using larger QM systems (∼340 atoms), the B3LYP density functional, and larger basis sets perform better, achieving mean signed errors down to -0.27 V. Compared to previous studies on iron-sulfur clusters, redox potentials for blue copper proteins show improved accuracy due to their narrower potential range and simpler coordination environments, but systematic errors are system-dependent. This study underscores the challenges of modeling redox-active sites in proteins and highlights the effectiveness of QM-cluster calculations in a continuum solvent in balancing computational cost with predictive power.