Energy Analysis of Zn Polycoordination in a Metalloprotein Environment and of the Role of a Neighboring Aromatic Residue. What Is the Impact of Polarization?

Force Field Parameterization of Actinyl Molecular Cations Using the 12-6-4 Model

In this work, a set of 12-6-4 force fields (FFs) parameters were developed for the actinyl molecular cations, AnO2n+ (n = 1, 2), from uranium to plutonium for classical molecular dynamics (MD) for four water models: TIP3P, SPC/E, OPC3, and TIP4Pew. Such a non-bonded potential model taking into account the induced dipole between the metallic center and the surrounding molecules has shown better performances for various cations than the classic 12-6 non-bonded potentials. The parametrization method proposed elsewhere for metallic cations has been extended to these molecular cations. In contrast to the actinyl 12-6 FFs from the literature, the new models reproduce correctly both solvation and thermodynamic properties, thanks to the inclusion of the induced dipole term (C4). The transferability of such force fields was assessed by performing MD simulations of carbonato actinyl species, which are highly implicated in actinide migration or actinide extraction from seawater. A highly satisfying agreement was found when comparing the EXAFS signals computed from our MD simulation to the experimental ones. The set of FFs developed here opens new possibilities for the study of actinide chemistry.

Upgrading and Validation of the AMBER Force Field for Histidine and Cysteine Zinc(II)-Binding Residues in Sites with Four Protein Ligands

We developed and validated a novel force field in the context of the AMBER parameterization for the simulation of zinc(II)-binding proteins. The proposed force field assumes nonbonded spherical interactions between the central zinc(II) and the coordinating residues. A crucial innovative aspect of our approach is to account for the polarization effects of the cation by redefining the atomic charges of the coordinating residues and an adjustment of Lennard-Jones parameters of Zn-interacting atoms to reproduce mean distance distributions. The optimal transferable parametrization was obtained by performing accurate quantum mechanical calculations on a training set of high-quality protein structures, encompassing the most common folds of zinc(II) sites. The addressed sites contain a zinc(II) ion tetra-coordinated by histidine and cysteine residues and represent about 70% of all physiologically relevant zinc(II) sites in the Protein Data Bank. Molecular dynamics simulations with explicit solvent, carried out on several zinc(II)-binding proteins not included in the training set, show that our model for zinc(II) sites preserves the tetra-coordination of the metal site with remarkable stability, yielding zinc(II)-X mean distances similar to experimental data. Finally, the model was tested by evaluating the zinc(II)-binding affinities, using the alchemical free energy perturbation approach. The calculated dissociation constants correlate satisfactorily with the experimental counterpart demonstrating the validity and transferability of the proposed parameterization for zinc(II)-binding proteins.

Temperature effect on the structure and conformational fluctuations in two zinc knuckles from the mouse mammary tumor virus

Zinc fingers are small protein domains in which zinc plays a structural role, contributing to the stability of the zinc-peptide complex. Zinc fingers are structurally diverse and are present in proteins that perform a broad range of functions in various cellular processes, such as replication and repair, transcription and translation, metabolism and signaling, cell proliferation, and apoptosis. Zinc fingers typically function as interaction modules and bind to a wide variety of compounds, such as nucleic acids, proteins, and small molecules. In this study, we investigated the structural properties, in solution, of the proximal and distal zinc knuckles of the nucleocapsid (NC) protein from the mouse mammary tumor virus (MMTV) (MMTV NC). For this purpose, we performed a series of molecular dynamics simulations in aqueous solution at 300 K, 333 K, and 348 K. The temperature effect was evaluated in terms of root mean square deviation of the backbone atoms and root mean square fluctuation of the coordinating residue atoms. The stability of the zinc coordination sphere was analyzed based upon the time profile of the interatomic distances between the zinc ions and the chelator atoms. The results indicate that the hydrophobic character of the proximal zinc finger is dominant at 333 K. The low mobility of the coordinating residues suggests that the strong electrostatic effect exerted by the zinc ion on its coordinating residues is not influenced by the increase in temperature. The evolution of the structural parameters of the coordination sphere of the distal zinc finger at 300 K gives us a reasonable picture of the unfolding pathway, as proposed by Bombarda and coworkers (Bombarda et al., 2005), which can predict the binding order of the four conserved ligand-binding residues. Our results support the conclusion that the structural features can vary significantly between the two zinc knuckles of MMTV NC.

Metal Ion Modeling Using Classical Mechanics

Metal ions play significant roles in numerous fields including chemistry, geochemistry, biochemistry, and materials science. With computational tools increasingly becoming important in chemical research, methods have emerged to effectively face the challenge of modeling metal ions in the gas, aqueous, and solid phases. Herein, we review both quantum and classical modeling strategies for metal ion-containing systems that have been developed over the past few decades. This Review focuses on classical metal ion modeling based on unpolarized models (including the nonbonded, bonded, cationic dummy atom, and combined models), polarizable models (e.g., the fluctuating charge, Drude oscillator, and the induced dipole models), the angular overlap model, and valence bond-based models. Quantum mechanical studies of metal ion-containing systems at the semiempirical, ab initio, and density functional levels of theory are reviewed as well with a particular focus on how these methods inform classical modeling efforts. Finally, conclusions and future prospects and directions are offered that will further enhance the classical modeling of metal ion-containing systems.

Parametrization of DFTB3/3OB for magnesium and zinc for chemical and biological applications

We report the parametrization of the approximate density functional theory, DFTB3, for magnesium and zinc for chemical and biological applications. The parametrization strategy follows that established in previous work that parametrized several key main group elements (O, N, C, H, P, and S). This 3OB set of parameters can thus be used to study many chemical and biochemical systems. The parameters are benchmarked using both gas-phase and condensed-phase systems. The gas-phase results are compared to DFT (mostly B3LYP), ab initio (MP2 and G3B3), and PM6, as well as to a previous DFTB parametrization (MIO). The results indicate that DFTB3/3OB is particularly successful at predicting structures, including rather complex dinuclear metalloenzyme active sites, while being semiquantitative (with a typical mean absolute deviation (MAD) of ∼3–5 kcal/mol) for energetics. Single-point calculations with high-level quantum mechanics (QM) methods generally lead to very satisfying (a typical MAD of ∼1 kcal/mol) energetic properties. DFTB3/MM simulations for solution and two enzyme systems also lead to encouraging structural and energetic properties in comparison to available experimental data. The remaining limitations of DFTB3, such as the treatment of interaction between metal ions and highly charged/polarizable ligands, are also discussed.

S/G-1: an ab initio force-field blending frozen Hermite Gaussian densities and distributed multipoles. Proof of concept and first applications to metal cations

We demonstrate as a proof of principle the capabilities of a novel hybrid MM'/MM polarizable force field to integrate short-range quantum effects in molecular mechanics (MM) through the use of Gaussian electrostatics. This lead to a further gain in accuracy in the representation of the first coordination shell of metal ions. It uses advanced electrostatics and couples two point dipole polarizable force fields, namely, the Gaussian electrostatic model (GEM), a model based on density fitting, which uses fitted electronic densities to evaluate nonbonded interactions, and SIBFA (sum of interactions between fragments ab initio computed), which resorts to distributed multipoles. To understand the benefits of the use of Gaussian electrostatics, we evaluate first the accuracy of GEM, which is a pure density-based Gaussian electrostatics model on a test Ca(II)-H2O complex. GEM is shown to further improve the agreement of MM polarization with ab initio reference results. Indeed, GEM introduces nonclassical effects by modeling the short-range quantum behavior of electric fields and therefore enables a straightforward (and selective) inclusion of the sole overlap-dependent exchange-polarization repulsive contribution by means of a Gaussian damping function acting on the GEM fields. The S/G-1 scheme is then introduced. Upon limiting the use of Gaussian electrostatics to metal centers only, it is shown to be able to capture the dominant quantum effects at play on the metal coordination sphere. S/G-1 is able to accurately reproduce ab initio total interaction energies within closed-shell metal complexes regarding each individual contribution including the separate contributions of induction, polarization, and charge-transfer. Applications of the method are provided for various systems including the HIV-1 NCp7-Zn(II) metalloprotein. S/G-1 is then extended to heavy metal complexes. Tested on Hg(II) water complexes, S/G-1 is shown to accurately model polarization up to quadrupolar response level. This opens up the possibility of embodying explicit scalar relativistic effects in molecular mechanics thanks to the direct transferability of ab initio pseudopotentials. Therefore, incorporating GEM-like electron density for a metal cation enable the introduction of nonambiguous short-range quantum effects within any point-dipole based polarizable force field without the need of an extensive parametrization.

Taking into Account the Ion-induced Dipole Interaction in the Nonbonded Model of Ions

Metal ions exist in almost half of the proteins in the protein databank and they serve as structural, electron-transfer and catalytic elements in the metabolic processes of organisms. Molecular Dynamics (MD) simulation is a powerful tool that provides information about biomolecular systems at the atomic level. Coupled with the growth in computing power, algorithms like the Particle Mesh Ewald (PME) method have become the accepted standard when dealing with long-range interactions in MD simulations. The nonbonded model of metal ions consists of an electrostatic plus 12-6 Lennard Jones (LJ) potential and is used largely because of its speed relative to more accurate models. In previous work we found that ideal parameters do not exist that reproduce several experimental properties for M(II) ions simultaneously using the nonbonded model coupled with the PME method due to the underestimation of metal ion-ligand interactions. Via a consideration of the nature of the nonbonded model, we proposed that the observed error largely arises from overlooking charge-induced dipole interactions. The electrostatic plus 12-6 LJ potential model works reasonably well for neutral systems but does struggle with more highly charged systems. In the present work we designed and parameterized a new nonbonded model for metal ions by adding a 1/r4 term to the 12-6 model. We call it the 12-6-4 LJ-type nonbonded model due to its mathematical construction. Parameters were determined for 16 +2 metal ions for the TIP3P, SPC/E and TIP4PEW water models. The final parameters reproduce the experimental hydration free energies (HFE), ion-oxygen distances (IOD) in the first solvation shell and coordination numbers (CN) accurately for the metal ions investigated. Preliminary tests on MgCl2 at different concentrations in aqueous solution and Mg2+--nucleic acid systems show reasonable results suggesting that the present parameters can work in mixed systems. The 12-6-4 LJ-type nonbonded model is readily adopted into standard force fields like AMBER, CHARMM and OPLS-AA with only a modest computational overhead. The new nonbonded model doesn't consider charge-transfer effects explicitly and, hence, may not suitable for the simulation of systems where charge-transfer effects play a decisive role.

Toward force fields for atomistic simulations of iridium-containing complexes

The structural and energetic characterization of metal complexes is important in catalysis and photochemical applications. Unraveling their modes-of-action can be greatly assisted by computation, which typically is restricted to computationally demanding methods including electronic structure calculations with density functional theory. Here, we present an empirical force field based on valence bond theory applicable to a range of octahedral Ir(III) complexes with different coordinating ligands, including iridium complexes with a chiral P,N ligand. Using an approach applicable to metal-containing complexes in general, it is shown that with one common parametrization 85% of the 116 diastereomers--all within 21 kcal/mol of the lowest energy conformation of each series--can be correctly ranked. For neutral complexes, all diastereomers are ranked correctly. This helps to identify the most relevant diastereomers which, if necessary, can be further investigated by more demanding computational methods. Furthermore, if one specific complex is considered, the root mean square deviation between reference data from electronic structure calculations and the force field is ≈1 kcal/mol. This, together with the possibility to carry out explicit simulations in solution paves the way for an atomistic understanding of iridium-containing complexes in catalysis.

A New Quantum Calibrated Force Field for Zinc-Protein Complex

A quantum calibrated polarizable-charge transfer force field (QPCT) has been proposed to accurately describe the interaction dynamics of zinc-protein complexes. The parameters of the QPCT force field were calibrated by quantum chemistry calculation and capture the polarization and charge transfer effect. QPCTs are validated by molecular dynamic simulation of the hydration shell of the zinc ion, five proteins containing the most common zinc-binding sites (ZnCys2His2, ZnCys3His1, ZnCys4, Zn2Cys6), as well as protein-ligand binding energy in zinc protein MMP3. The calculated results show excellent agreement with the experimental measurement and with results from QM/MM simulation, demonstrating that QPCT is accurate enough to maintain the correct structural integrity of the zinc binding pocket and provide accurate interaction dynamics of the zinc-residue complex. The current approach can also be extended to the study of interaction dynamics of other metal-containing proteins by recalibrating the corresponding parameters to the specific complexes.

A Transferable Non-bonded Pairwise Force Field to Model Zinc Interactions in Metalloproteins

Herein we introduce a novel practical strategy to overcome the well-known challenge of modeling the divalent zinc cation in metalloproteins. The main idea is to design short-long effective functions (SLEF) to describe charge interactions between the zinc ion and all other atoms. This SLEF approach has the following desired features: (1). It is pairwise, additive and compatible with widely used atomic pair-wise force fields for modeling biomolecules; (2). It only changes interactions between the zinc ion and other atoms, and does not affect force field parameters that model other interactions in the system; (3). It is a non-bonded model that is inherently capable to describe different zinc ligands and coordination modes. By optimizing two SLEF parameters as well as zinc vdW parameters through force matching based on Born-Oppenheimer ab initio QM/MM molecular dynamics simulations, we have successfully developed the first SLEF force field (SLEF1) to describe zinc interactions. Extensive molecular dynamics simulations of seven zinc enzyme systems with different coordination ligands and distinct chelation modes (4-,5-,6-fold), including the binuclear zinc active site, yielded zinc coordination numbers and binding distances in good agreement with the corresponding crystal structures as well as ab initio QM/MM MD results. This not only demonstrates the transferability and adequacy of the new SLEF1 force field in describing a variety of zinc proteins, but also indicates that this novel SLEF approach is a promising direction to explore for improving force field description of metal ion interactions.

Polarizable molecular dynamics simulation of Zn(II) in water using the AMOEBA force field

The hydration free energy, structure, and dynamics of the zinc divalent cation are studied using a polarizable force field in molecular dynamics simulations. Parameters for the Zn(2+) are derived from gas-phase ab initio calculation of Zn(2+)-water dimer. The Thole-based dipole polarization is adjusted based on the Constrained Space Orbital Variations (CSOV) calculation while the Symmetry Adapted Perturbation Theory (SAPT) approach is also discussed. The vdW parameters of Zn(2+) have been obtained by comparing the AMOEBA Zn(2+)-water dimerization energy with results from several theory levels and basis sets over a range of distances. Molecular dynamics simulations of Zn(2+) solvation in bulk water are subsequently performed with the polarizable force field. The calculated first-shell water coordination number, water residence time and free energy of hydration are consistent with experimental and previous theoretical values. The study is supplemented with extensive Reduced Variational Space (RVS) and Electron Localization Function (ELF) computations in order to unravel the nature of the bonding in Zn(2+)(H(2)O)(n) (n=1,6) complexes and to analyze the charge transfer contribution to the complexes. Results show that the importance of charge transfer decreases as the size of Zn-water cluster grows due to anticooperativity and to changes in the nature of the metal-ligand bonds. Induction could be dominated by polarization when the system approaches condensed-phase and the covelant effects are eliminated from the Zn(II)-water interaction. To construct an "effective" classical polarizable potential for Zn(2+) in bulk water, one should therefore avoid over-fitting to the ab initio charge transfer energy of Zn(2+)-water dimer. Indeed, in order to avoid overestimation of condensed-phase many-body effects, which is crucial to the transferability of polarizable molecular dynamics, charge transfer should not be included within the classical polarization contribution and should preferably be either incorporated in to the pairwise van der Waals contribution or treated explicitly.