Quantum Effects in Cation Interactions with First and Second Coordination Shell Ligands in Metalloproteins

Despite decades of investigations, the principal mechanisms responsible for the high affinity and specificity of proteins for key physiological cations K⁺, Na⁺, and Ca²⁺ remain a hotly debated topic. At the core of the debate is an apparent need (or lack thereof) for an accurate description of the electrostatic response of the charge distribution in a protein to the binding of an ion. These effects range from partial electronic polarization of the directly ligating atoms to long-range effects related to partial charge transfer and electronic delocalization effects. While accurate modeling of cation recognition by metalloproteins warrants the use of quantum-mechanics (QM) calculations, the most popular approximations used in major biomolecular simulation packages rely on the implicit modeling of electronic polarization effects. That is, high-level QM computations for ion binding to proteins are desirable, but they are often unfeasible, because of the large size of the reactive-site models and the need to sample conformational space exhaustively at finite temperature. Several solutions to this challenge have been proposed in the field, ranging from the recently developed Drude polarizable force-field for simulations of metalloproteins to approximate tight-binding density functional theory (DFTB). To delineate the usefulness of different approximations, we examined the accuracy of three recent and commonly used theoretical models and numerical algorithms, namely, CHARMM C36, the latest developed Drude polarizable force fields, and DFTB3 with the latest 3OB parameters. We performed MD simulations for 30 cation-selective proteins with high-resolution X-ray structures to create ensembles of structures for analysis with different levels of theory, e.g., additive and polarizable force fields, DFTB3, and DFT. The results from DFT computations were used to benchmark CHARMM C36, Drude, and DFTB3 performance. The explicit modeling of quantum effects unveils the key electrostatic properties of the protein sites and the importance of specific ion-protein interactions. One of the most interesting findings is that secondary coordination shells of proteins are noticeably perturbed in a cation-dependent manner, showing significant delocalization and long-range effects of charge transfer and polarization upon binding Ca<sup>2+