Toward a new approach for determination of solute's charge distribution to analyze interatomic electrostatic interactions in quantum mechanical/molecular mechanical simulations

We present an alternative approach to determine "density-dependent property"-derived charges for molecules in the condensed phase. In the case of a solution, it is essential to take into consideration the electron polarization of molecules in the active site of this system. The solute and solvent molecules in this site have to be described by a quantum mechanical technique and the others are allowed to be treated by a molecular mechanical method (QM/MM scheme). For calculations based on this scheme, using the forces and interaction energy as density-dependent property our charges from interaction energy and forces (CHIEF) approach can provide the atom-centered charges on the solute atoms. These charges reproduce well the electrostatic potentials around the solvent molecules and present properly the picture of the electron density of the QM subsystem in the solution system. Thus, the CHIEF charges can be considered as the atomic charges under the conditions of the QM/MM simulation, and then enable one to analyze electrostatic interactions between atoms in the QM and MM regions. This approach would give a view of the QM nuclei and electrons different from the conventional methods.     

Quantum mechanics/molecular mechanics electrostatic embedding with continuous and discrete functions

A quantum mechanics/molecular mechanics (QM/MM) implementation that uses the Gaussian electrostatic model (GEM) as the MM force field is presented. GEM relies on the reproduction of electronic density by using auxiliary basis sets to calculate each component of the intermolecular interaction. This hybrid method has been used, along with a conventional QM/MM (point charges) method, to determine the polarization on the QM subsystem by the MM environment in QM/MM calculations on 10 individual H(2)O dimers and a Mg(2+)-H(2)O dimer. We observe that GEM gives the correct polarization response in cases when the MM fragment has a small charge, while the point charges produce significant over-polarization of the QM subsystem and in several cases present an opposite sign for the polarization contribution. In the case when a large charge is located in the MM subsystem, for example, the Mg(2+) ion, the opposite is observed at small distances. However, this is overcome by the use of a damped Hermite charge, which provides the correct polarization response.     

Conformational dependence of charges in protein simulations

We have studied the conformational dependence of molecular mechanics atomic charges for proteins by calculating the charges fitted to the quantum mechanical (QM) electrostatic potential (ESP) for all atoms in complexes between avidin and seven biotin analogues for 20 snapshots from molecular dynamics simulations. We have studied how various other charge sets reproduce those charges. The QM charges, even if averaged over all snapshots or all residues, in general have a larger magnitude than standard Amber charges, indicating that the restraint toward zero in the restrained ESP method is too strong. This has a significant influence on the electrostatic conformational energies and the interaction energy between the biotin ligand and the protein, giving a difference between the QM and Amber charges of 43 and 8 kJ/mol for the negatively charged and neutral biotin analogues, respectively (3-4%). However, this energy difference is strongly reduced if the solvation energy (calculated by the Poisson-Boltzmann or Generalized Born methods) is added, viz., to 7 kJ/mol for charged and 3 kJ/mol for uncharged ligand. In fact, charges need to be recalculated with a QM method only for residues within 7 or 4 A of the ligand, if the error should be less than 4 kJ/mol. Unfortunately, the QM charges do not give significantly better MM/PBSA estimates of ligand-binding affinities than standard Amber charges.     

Toward a consistent treatment of polarization in model QM/MM calculations

The concept of model chemistries within hybrid QM/MM calculations has been addressed through analysis of the polarization energy determined by two distinct approaches based on (i) induced charges and (ii) induced dipoles. The quantum mechanical polarization energy for four configurations of the water dimer has been determined for a range of basis sets using Morokuma energy decomposition analysis. This benchmark value has been compared to the fully classical polarization energy determined using the induced dipole approach, and the molecular mechanics polarization energy calculated using induced charges within the MM region of hybrid QM/MM calculations. From the water dimer calculations, it is concluded that the induced charge approach is consistent with medium sized basis set calculations whereas the induced dipole approach is consistent with large basis set calculations. This result is highly relevant to the concept of QM/MM model chemistries.     

Molecular dynamics and free energy perturbation study of hydride-ion transfer step in dihydrofolate reductase using combined quantum and molecular mechanical model

We used molecular dynamics simulation and free energy perturbation (FEP) methods to investigate the hydride-ion transfer step in the mechanism for the nicotinamide adenine dinucleotide phosphate (NADPH)-dependent reduction of a novel substrate by the enzyme dihydrofolate reductase (DHFR). The system is represented by a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1 semiempirical molecular orbital method for the reacting substrate and NADPH cofactor fragments, the AMBER force field for DHFR, and the TIP3P model for solvent water. The FEP calculations were performed for a number of choices for the QM system. The substrate, 8-methylpterin, was treated quantum mechanically in all the calculations, while the larger cofactor molecule was partitioned into various QM and MM regions with the addition of “link” atoms (F, CH₃, and H). Calculations were also carried out with the entire NADPH molecule treated by QM. The free energies of reaction and the net charges on the NADPH fragments were used to determine the most appropriate QM/MM model. The hydride-ion transfer was also carried out over several FEP pathways, and the QM and QM/MM component free energies thus calculated were found to be state functions (i.e., independent of pathway). A ca. 10 kcal/mol increase in free energy for the hydride-ion transfer with an activation barrier of ca. 30 kcal/mol was calculated. The increase in free energy on the hydride-ion transfer arose largely from the QM/MM component. Analysis of the QM/MM energy components suggests that, although a number of charged residues may contribute to the free energy change through long-range electrostatic interactions, the only interaction that can account for the 10 kcal/mol increase in free energy is the hydrogen bond between the carboxylate side chain of Glu30 (avian DHFR) and the activated (protonated) substrate. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 977–988, 1998     

Coupled semiempirical quantum mechanics and molecular mechanics (QM/MM) calculations on the aqueous solvation free energies of ionized molecules

The aqueous solvation free energies of ionized molecules were computed using a coupled quantum mechanical and molecular mechanical (QM/MM) model based on the AM1, MNDO, and PM3 semiempirical molecular orbital methods for the solute molecule and the TIP3P molecular mechanics model for liquid water. The present work is an extension of our model for neutral solutes where we assumed that the total free energy is the sum of components derived from the electrostatic/polarization terms in the Hamiltonian plus an empirical “nonpolar” term. The electrostatic/polarization contributions to the solvation free energies were computed using molecular dynamics (MD) simulation and thermodynamic integration techniques, while the nonpolar contributions were taken from the literature. The contribution to the electrostatic/polarization component of the free energy due to nonbonded interactions outside the cutoff radii used in the MD simulations was approximated by a Born solvation term. The experimental free energies were reproduced satisfactorily using variational parameters from the vdW terms as in the original model, in addition to a parameter from the one-electron integral terms. The new one-electron parameter was required to account for the short-range effects of overlapping atomic charge densities. The radial distribution functions obtained from the MD simulations showed the expected H-bonded structures between the ionized solute molecule and solvent molecules. We also obtained satisfactory results by neglecting both the empirical nonpolar term and the electronic polarization of the solute, i.e., by implementing a nonpolarization model. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1028–1038, 1999     

Reaction path potential for complex systems derived from combined ab initio quantum mechanical and molecular mechanical calculations

Combined ab initio quantum mechanical and molecular mechanical calculations have been widely used for modeling chemical reactions in complex systems such as enzymes, with most applications being based on the determination of a minimum energy path connecting the reactant through the transition state to the product in the enzyme environment. However, statistical mechanics sampling and reaction dynamics calculations with a combined ab initio quantum mechanical (QM) and molecular mechanical (MM) potential are still not feasible because of the computational costs associated mainly with the ab initio quantum mechanical calculations for the QM subsystem. To address this issue, a reaction path potential energy surface is developed here for statistical mechanics and dynamics simulation of chemical reactions in enzymes and other complex systems. The reaction path potential follows the ideas from the reaction path Hamiltonian of Miller, Handy and Adams for gas phase chemical reactions but is designed specifically for large systems that are described with combined ab initio quantum mechanical and molecular mechanical methods. The reaction path potential is an analytical energy expression of the combined quantum mechanical and molecular mechanical potential energy along the minimum energy path. An expansion around the minimum energy path is made in both the nuclear and the electronic degrees of freedom for the QM subsystem internal energy, while the energy of the subsystem described with MM remains unchanged from that in the combined quantum mechanical and molecular mechanical expression and the electrostatic interaction between the QM and MM subsystems is described as the interaction of the MM charges with the QM charges. The QM charges are polarizable in response to the changes in both the MM and the QM degrees of freedom through a new response kernel developed in the present work. The input data for constructing the reaction path potential are energies, vibrational frequencies, and electron density response properties of the QM subsystem along the minimum energy path, all of which can be obtained from the combined quantum mechanical and molecular mechanical calculations. Once constructed, it costs much less for its evaluation. Thus, the reaction path potential provides a potential energy surface for rigorous statistical mechanics and reaction dynamics calculations of complex systems. As an example, the method is applied to the statistical mechanical calculations for the potential of mean force of the chemical reaction in triosephosphate isomerase.     

Effect of polarization on the opsin shift in rhodopsins. 2. Empirical polarization models for proteins

The explicit treatment of polarization as a many-body interaction in condensed-phase systems represents a current problem in empirical force-field development. Although a variety of efficient models for molecular polarization have been suggested, polarizable force fields are still far from common use nowadays. In this work, we consider interactive polarization models employing Thole's short-range damping scheme and assess them for application on polypeptides. Despite the simplicity of the model, we find mean polarizabilities and anisotropies of amino acid side chains in excellent agreement with MP2/cc-pVQZ benchmark calculations. Combined with restrained electrostatic potential (RESP) derived atomic charges, the models are applied in a quantum-mechanical/molecular-mechanical (QM/MM) approach. An iterative scheme is used to establish a self-consistent mutual polarization between the QM and MM moieties. This ansatz is employed to study the influence of the protein polarizability on calculated optical properties of the protonated Schiff base of retinal in rhodopsin (Rh), bacterio-rhodopsin (bR), and pharaonis sensory rhodopsin II (psRII). The shifts of the excitation energy due to the instantaneous polarization response of the protein to the charge transfer on the retinal chromophore are quantified using the high level ab initio multireference spectroscopy-oriented configuration interaction (SORCI) method. The results are compared with those of previously published QM1/QM2/MM models for bR and psRII.     

Performance assessment of semiempirical molecular orbital methods in describing halogen bonding: quantum mechanical and quantum mechanical/molecular mechanical-molecular dynamics study

The performance of semiempirical molecular-orbital methods--MNDO, MNDO-d, AM1, RM1, PM3 and PM6--in describing halogen bonding was evaluated, and the results were compared with molecular mechanical (MM) and quantum mechanical (QM) data. Three types of performance were assessed: (1) geometrical optimizations and binding energy calculations for 27 halogen-containing molecules complexed with various Lewis bases (Two of the tested methods, AM1 and RM1, gave results that agree with the QM data.); (2) charge distribution calculations for halobenzene molecules, determined by calculating the solvation free energies of the molecules relative to benzene in explicit and implicit generalized Born (GB) solvents (None of the methods gave results that agree with the experimental data.); and (3) appropriateness of the semiempirical methods in the hybrid quantum-mechanical/molecular-mechanical (QM/MM) scheme, investigated by studying the molecular inhibition of CK2 protein by eight halobenzimidazole and -benzotriazole derivatives using hybrid QM/MM molecular-dynamics (MD) simulations with the inhibitor described at the QM level by the AM1 method and the rest of the system described at the MM level. The pure MM approach with inclusion of an extra point of positive charge on the halogen atom approach gave better results than the hybrid QM/MM approach involving the AM1 method. Also, in comparison with the pure MM-GBSA (generalized Born surface area) binding energies and experimental data, the calculated QM/MM-GBSA binding energies of the inhibitors were improved by replacing the G(GB,QM/MM) solvation term with the corresponding G(GB,MM) term.     

Geometry optimization using tuned and balanced redistributed charge schemes for combined quantum mechanical and molecular mechanical calculations

We performed geometry optimizations using the tuned and balanced redistributed charge algorithms to treat the QM-MM boundary in combined quantum mechanical and molecular mechanical (QM/MM) methods. In the tuned and balanced redistributed charge (TBRC) scheme, the QM boundary atom is terminated by a tuned F link atom, and the charge of the MM boundary atom is properly adjusted to conserve the total charge of the entire QM/MM system; then the adjusted MM boundary charge is moved evenly to the midpoints of the bonds between the MM boundary atom and its neighboring MM atoms. In the tuned and balanced redistributed charge-2 (TBRC2) scheme, the adjusted MM boundary charge is moved evenly to all MM atoms that are attached to the MM boundary atom. A new option, namely charge smearing, has been added to the TBRC scheme, yielding the tuned and balanced smeared redistributed charge (TBSRC) scheme. In the new scheme, the redistributed charges near the QM-MM boundary are smeared to make the electrostatic interactions between the QM region and the redistributed charges more realistic. The TBRC2 scheme and new TBSRC scheme have been tested for various kinds of bonds at a QM-MM boundary, including C-C, C-N, C-O, O-C, N-C, C-S, S-S, S-C, C-Si, and O-N bonds. Charge smearing is necessary if the redistributed charges are close to the QM region, as in the TBSRC scheme, but not if the redistributed charge is farther from the QM region, as in the TBRC2 scheme. We found that QM/MM results using either the TBRC2 scheme or the TBSRC scheme agree well with full QM results; the mean unsigned error (MUE) of the QM/MM deprotonation energy is 1.6 kcal/mol in both cases, and the MUE of QM/MM optimized bond lengths over the three bonds closest to the QM-MM boundary, with errors averaged over the protonated forms and unprotonated forms, is 0.015 ? for TBRC2 and 0.021 ? for TBSRC. The improvements in the new scheme are essential for QM-MM boundaries that pass through a polar bond, but even for boundaries that pass through C-C bonds, the improvement can be quite significant.     

A numerically stable restrained electrostatic potential charge fitting method

Inspired by the idea of charge decomposition in calculation of the dipole preserving and polarization consistent charges (Zhang et al., J. Comput. Chem. 2011, 32, 2127), we have proposed a numerically stable restrained electrostatic potential (ESP)‐based charge fitting method for protein. The atomic charge is composed of two parts. The dominant part is fixed to a predefined value (e.g., AMBER charge), and the residual part is to be determined by restrained fitting to residual ESP on grid points around the molecule. Nonuniform weighting factors as a function of the dominant charge are assigned to the atoms. Because the residual part is several folds to several orders smaller than the dominant part, the impact of ill‐conditioning is alleviated. This charge fitting method can be used in quantum mechanical/molecular mechanical (QM/MM) simulations and similar studies, where QM calculated electronic properties are frequently mapped to partial atomic charges. © 2012 Wiley Periodicals, Inc.     

Solvation Free Energy Calculations: The Combination between the Implicitly Polarized Fixed-charge Model and the Reference Potential Strategy

The IPolQ-Mod charges, which are the average of two charge sets fitted in vacuum state and condensed phase, take account of polarization effect implicitly in the solvation free energy calculation. However, the performance of the IPolQ-Mod charges sensitively depends on the QM levels used to generate the electrostatic potential from which the charges are fitted. In addition, the forces on atoms are not accurate theoretically in the molecular dynamics (MD) simulation as the solvent only feels the electrostatic potential of a half-polarized density of the solute according to the derivation of the IPolQ-Mod charges. To study these issues in detail, the IPolQ-Mod charges are combined with the reference potential (RP) strategy to predict the solvation free energies in the present study. It is found that the thermodynamic perturbation (TP) corrections utilizing total energy difference and interaction energy difference are almost the same and free of bias. The solvation free energies estimated by the RP method match very well with those obtained by applying IPolQ-Mod charges into MD simulation directly. By means of the RP strategy, the performances of the IPolQ-Mod charges with the change of the strength of the exact HF exchange in several DFT functionals are determined effectively. Although the “optimal” strengths are found in B3LYP and LC-ωPBE, the improvements over the default strength are not too much. In addition to the IPolQ-Mod charges, other charge models like bond charge correction (BCC) charges could also be combined with the RP strategy to study the thermodynamic properties like solvation free energy. © 2019 Wiley Periodicals, Inc.     

YinYang atom: a simple combined ab initio quantum mechanical molecular mechanical model

A simple interface is proposed for combined quantum mechanical (QM) molecular mechanical (MM) calculations for the systems where the QM and MM regions are connected through covalent bonds. Within this model, the atom that connects the two regions, called YinYang atom here, serves as an ordinary MM atom to other MM atoms and as a hydrogen-like atom to other QM atoms. Only one new empirical parameter is introduced to adjust the length of the connecting bond and is calibrated with the molecule propanol. This model is tested with the computation of equilibrium geometries and protonation energies for dozens of molecules. Special attention is paid on the influence of MM point charges on optimized geometry and protonation energy, and it is found that it is important to maintain local charge-neutrality in the MM region in order for the accurate calculation of the protonation and deprotonation energies. Overall the simple YinYang atom model yields comparable results to some other QM/MM models.     

Importance of accurate charges in molecular docking: quantum mechanical/molecular mechanical (QM/MM) approach

The extent to which accuracy of electric charges plays a role in protein-ligand docking is investigated through development of a docking algorithm, which incorporates quantum mechanical/molecular mechanical (QM/MM) calculations. In this algorithm, fixed charges of ligands obtained from force field parameterization are replaced by QM/MM calculations in the protein environment, treating only the ligands as the quantum region. The algorithm is tested on a set of 40 cocrystallized structures taken from the Protein Data Bank (PDB) and provides strong evidence that use of nonfixed charges is important. An algorithm, dubbed "Survival of the Fittest" (SOF) algorithm, is implemented to incorporate QM/MM charge calculations without any prior knowledge of native structures of the complexes. Using an iterative protocol, this algorithm is able in many cases to converge to a nativelike structure in systems where redocking of the ligand using a standard fixed charge force field exhibits nontrivial errors. The results demonstrate that polarization effects can play a significant role in determining the structures of protein-ligand complexes, and provide a promising start towards the development of more accurate docking methods for lead optimization applications.     

Study of lithium cation in water clusters: based on atom-bond electronegativity equalization method fused into molecular mechanics

We present a potential model for Li(+)-water clusters based on a combination of the atom-bond electronegativity equalization and molecular mechanics (ABEEM/MM) that is to take ABEEM charges of the cation and all atoms, bonds, and lone pairs of water molecules into the intermolecular electrostatic interaction term in molecular mechanics. The model allows point charges on cationic site and seven sites of an ABEEM-7P water molecule to fluctuate responding to the cluster geometry. The water molecules in the first sphere of Li(+) are strongly structured and there is obvious charge transfer between the cation and the water molecules; therefore, the charge constraint on the ionic cluster includes the charged constraint on the Li(+) and the first-shell water molecules and the charge neutrality constraint on each water molecule in the external hydration shells. The newly constructed potential model based on ABEEM/MM is first applied to ionic clusters and reproduces gas-phase state properties of Li(+)(H(2)O)(n) (n = 1-6 and 8) including optimized geometries, ABEEM charges, binding energies, frequencies, and so on, which are in fair agreement with those measured by available experiments and calculated by ab initio methods. Prospects and benefits introduced by this potential model are pointed out.     

Hybrid density functional theory/molecular mechanics calculations of two-photon absorption of dimethylamino nitro stilbene in solution

The dimethylamino nitro stilbene (DANS) molecule is studied for exploring solvent effects on two-photon absorption using the quantum mechanical/molecular mechanical (QM/MM) response theory approach, where the quantum part is represented by density functional theory. We have explored the role of geometrical change of the chromophore in solution, the importance of taking a dynamical average over the sampled structures and the role of a granular representation of the polarization and electrostatic interactions with the classically described medium. The line shape function was simulated by the QM/MM technique thereby allowing for non-empirical prediction of the absolute two-photon cross section. We report a maximum in the TPA cross section for a medium of intermediate solvent polarity (i.e. in chloroform) and provide the grounds for an explanation of this effect which recently has been experimentally observed for a series of charge transfer species in solvents of different polarity. The calculations of absorption energies reproduce well the positive solvatochromic behavior of DANS and are in good agreement with experimental spectra available for the chloroform and DMSO solvents. In line with recent development of the QM/MM response technique for color modeling, we find this methodology to offer a versatile tool to predict and analyze two-photon absorption phenomena taking place within a medium.     

Incorporation of a QM/MM buffer zone in the variational double self-consistent field method

The explicit polarization (X-Pol) potential is an electronic-structure-based polarization force field, designed for molecular dynamics simulations and modeling of biopolymers. In this approach, molecular polarization and charge transfer effects are explicitly treated by a combined quantum mechanical and molecular mechanical (QM/MM) scheme, and the wave function of the entire system is variationally optimized by a double self-consistent field (DSCF) method. In the present article, we introduce a QM buffer zone for a smooth transition from a QM region to an MM region. Instead of using the Mulliken charge approximation for all QM/MM interactions, the Coulombic interactions between the adjacent fragments are determined directly by electronic structure theory. The present method is designed to accelerate the speed of convergence of the total energy and charge density of the system.