Reliable Redox-Potential Simulations of Proteins

The computation of protein redox potentials is crucial for understanding various biological processes but is challenging due to very large system sizes precluding full quantum mechanical (QM) treatment. Commonly applied hybrid quantum mechanical/molecular mechanics (QM/MM) methods are often unsuitable due to nonpolarizable force fields, making pure QM calculations on cluster models a better choice. However, truncating a solvated protein with several thousand atoms to a small cluster model introduces potential sources of error. In the present study, redox properties were computed with density functional theory (DFT) for a diverse set of ten proteins using cluster models of varying sizes, ranging from 200 to 1500 atoms, including full protein calculations. Our results show that cluster models containing approximately 500 atoms are sufficient, as truncation errors become smaller than the typical DFT errors beyond that size. Additionally, we computed the standard redox potentials of ten proteins using the 500-atom cluster models within a snapshot-based approach, grounded in Marcus theory. In the proposed snapshot approach, QM/MM geometry optimizations were performed on snapshots from a classical molecular dynamics trajectory. The QM/MM geometries were truncated to 500-atom cluster models, and redox potentials were computed from vertical reduction energies using DFT. Comparison with experimental redox potentials revealed a mean absolute error (MAE) of 0.12 V, achieved without any reference or calibration calculations, which is only slightly larger than the previously estimated intrinsic DFT error. In contrast, QM/MM energies yielded rather unreliable results, with an MAE of 0.36 V for standard redox potentials. These findings are not only significant for improving redox potential predictions but also broadly relevant for electronic structure calculations in complex systems involving charge changes, such as protonation/deprotonation processes, electron transfer processes, and electrocatalysis.