Quantum Chemical Topology Analysis of Covalent Interactions in the Hydration of F<sup>-</sup> along with the Zinc Finger of NPL4 and Its Application to the Delimitation of QM/MM Boundaries.

Abstract

The accurate modeling of metalloproteins remains a central challenge in computational chemistry, particularly when classical force fields fail to describe metal-ligand interactions with significant covalent character. Herein, we present a diagnostic methodology to delimit quantum mechanical regions in hybrid quantum mechanics/molecular mechanics (QM/MM) simulations, considering (i) the hydration of F^- and (ii) the zinc finger (ZF) domain of the Nuclear Protein Localization 4 (NPL4) as case studies. Our approach is grounded in methods of wave function analysis within quantum chemical topology. Specifically, we rely on the quantum theory of atoms in molecules and the interacting quantum atoms approaches to partition interaction energies between (i) the F^- anions and solvating water molecules and (ii) the Zn²⁺ and its surrounding amino acids within the ZF of NPL4 into classical (ionic) and exchange-correlation (covalent) components. The presented methodology provides also a rational criterion to determine either the inclusion or exclusion of water molecules within the QM region as Zn²⁺···OH₂ interactions might be relevant as indicated by electronic structure geometry optimizations. Our diagnostic offers a systematic way to define suitable QM/MM boundaries, and it is useful to decide on the inclusion of solvent or other species in the QM region of hybrid simulations when covalent contributions are uncertain or only partially present. This analysis reveals that (i) the first solvation layer of F^- and (ii) the first coordination shell of Zn²⁺ exhibit significant covalency in their interaction with the F^- and Zn²⁺ ions, respectively, justifying a minimal QM region comprising three cysteines, one histidine, and the metal center for the ZF in NPL4. The QM/MM hybrid simulations for the hydration of the F^- anion showed important differences with respect to classical molecular mechanics concerning the coordination number and maxima of F^-···O peaks in the radial distribution functions. Hybrid QM/MM simulations using this covalency-based region in the ZF of NPL4 recover accurate coordination geometries and bond lengths, correcting important distortions introduced by classical force fields, including spurious hydration and hypercoordination of the Zn²⁺ center. Both the enlargement and reduction of the QM region result in incorrect coordination geometries and less accurate Zn²⁺-ligand distance distributions. The diagnostic method put forward herein shows that metrics based on the chemical bonding scenario can inform the construction of transferable QM regions for the solvation of ions and metalloproteins. Overall, our results establish a general protocol to integrate wave function analysis with hybrid modeling, and they highlight the potential of such analysis to improve the accuracy of QM/MM simulations.