Influence of inter- and intramolecular hydrogen bonding on kemp decarboxylations from QM/MM simulations

The Kemp decarboxylation reaction for benzisoxazole-3-carboxylic acid derivatives has been investigated using QM/MM calculations in protic and dipolar aprotic solvents. Aprotic solvents have been shown to accelerate the rates of reaction by 7-8 orders of magnitude over water; however, the inclusion of an internal hydrogen bond effectively inhibits the reaction with near solvent independence. The effects of solvation and intramolecular hydrogen bonding on the reactants, transition structures, and the rate of reaction are elucidated using two-dimensional potentials of mean force (PMF) derived from free energy perturbation calculations in Monte Carlo simulations (MC/FEP). Free energies of activation in six solvents have been computed to be in close agreement with experiment. Solute-solvent interaction energies show that poorer solvation of the reactant anion in the dipolar aprotic solvents is primarily responsible for the observed rate enhancements over protic media. In addition, a discrepancy for the experimental rate in chloroform has been studied in detail with the conclusion that ion-pairing between the reactant anion and tetramethylguanidinium counterion is responsible for the anomalously slow reaction rate. The overall quantitative success of the computations supports the present QM/MM/MC approach, which features PDDG/PM3 as the QM method.     

Solvent effects and mechanism for a nucleophilic aromatic substitution from QM/MM simulations

The nucleophilic aromatic substitution (SNAr) reaction between azide ion and 4-fluoronitrobenzene has been investigated using QM/MM and DFT/PCM calculations in protic and dipolar aprotic solvents. The effects of solvation on the transition structures, the intermediate Meisenheimer complex, and the rate of reaction are elucidated. The large rate increases in proceeding from protic to dipolar aprotic solvents are only reproduced by the QM/MM methodology.     

A new solvent-dependent mechanism for a triazolinedione ene reaction

The ene reaction between 4-phenyl-1,2,4-triazoline-3,5-dione (PTAD) and tetramethylethylene has been investigated using QM/MM calculations in water, methanol, DMSO, and acetonitrile. The effects of solvation on the mechanism and rates of reaction are elucidated using two-dimensional potentials of mean force (PMF) simulations utilizing free-energy perturbation theory and Monte Carlo statistical mechanics. A new mechanism is proposed where direct formation of an open dipolar intermediate following the addition of PTAD to the alkene is rate-limiting and the pathway toward ene product is significantly dependent on the reaction medium. In protic solvents, the open dipolar intermediate may proceed directly to the ene product or reversibly form an aziridinium imide (AI) intermediate that does not participate in the reaction. However, in aprotic solvents the open intermediate is short-lived (<10-11 s) and the ene product forms via the AI intermediate. The calculated free energies of activation are in close agreement with those derived from experiment, e.g., DeltaG of 14.9 kcal/mol compared to 15.0 kcal/mol in acetonitrile. Density functional theory calculations at the (U)B3LYP/6-311++G(2d,p) level using the CPCM continuum solvent model were also carried out and confirmed a zwitterionic, and not diradical, open intermediate present in the reaction. Only the QM/MM methodology was able to accurately reproduce the experimental rates and differentiate between the protic and aprotic solvents. Solute-solvent interaction energies, radial distribution functions, and charges are analyzed and show that the major factor dictating the changes in reaction path is hydrogen bond stabilization of the charge separations spanning 2 to 4 atoms in the intermediates and transition states.     

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.     

Investigation of solvent effects for the Claisen rearrangement of chorismate to prephenate: mechanistic interpretation via near attack conformations

Solvent effects on the rate of the Claisen rearrangement of chorismate to prephenate have been examined in water and methanol. The preequilibrium free-energy differences between diaxial and diequatorial conformers of chorismate, which had previously been implicated as the sole basis for the observed 100-fold rate increase in water over methanol, have been reframed using the near attack conformation (NAC) concept of Bruice and co-workers. Using a combined QM/MM Monte Carlo/free-energy perturbation (MC/FEP) method, 82%, 57%, and 1% of chorismate conformers were found to be NAC structures (NACs) in water, methanol, and the gas phase, respectively. As a consequence, the conversion of non-NACs to NACs provides no free-energy contributions to the overall relative reaction rates in water versus methanol. Free-energy perturbation calculations yielded differences in free energies of activation for the two polar protic solvents and the gas phase. The rate enhancement in water over the gas phase arises from preferential hydration of the transition state (TS) relative to the reactants via increased hydrogen bonding and long-range electrostatic interactions, which accompany bringing the two negatively charged carboxylates into closer proximity. More specifically, there is an increase of 1.3 and 0.6 hydrogen bonds to the carboxylate groups and the ether oxygen, respectively, in going from the reactant to the TS in water. In methanol, the corresponding changes in hydrogen bonding with first shell solvent molecules are small; the rate enhancement arises primarily from the enhanced long-range interactions with solvent molecules. Thus, the reaction occurs faster in water than in methanol due to greater stabilization of the TS in water by specific interactions with first shell solvent molecules.     

Convergence in the QM‐only and QM/MM modeling of enzymatic reactions: A case study for acetylene hydratase

We report systematic quantum mechanics‐only (QM‐only) and QM/molecular mechanics (MM) calculations on an enzyme‐catalyzed reaction to assess the convergence behavior of QM‐only and QM/MM energies with respect to the size of the chosen QM region. The QM and MM parts are described by density functional theory (typically B3LYP/def2‐SVP) and the CHARMM force field, respectively. Extending our previous work on acetylene hydratase with QM regions up to 157 atoms (Liao and Thiel, J. Chem. Theory Comput. 2012, 8, 3793), we performed QM/MM geometry optimizations with a QM region M4 composed of 408 atoms, as well as further QM/MM single‐point calculations with even larger QM regions up to 657 atoms. A charge deletion analysis was conducted for the previously used QM/MM model ( M3a , with a QM region of 157 atoms) to identify all MM residues with strong electrostatic contributions to the reaction energetics (typically more than 2 kcal/mol), which were then included in M4 . QM/MM calculations with this large QM region M4 lead to the same overall mechanism as the previous QM/MM calculations with M3a , but there are some variations in the relative energies of the stationary points, with a mean absolute deviation (MAD) of 2.7 kcal/mol. The energies of the two relevant transition states are close to each other at all levels applied (typically within 2 kcal/mol), with the first (second) one being rate‐limiting in the QM/MM calculations with M3a ( M4 ). QM‐only gas‐phase calculations give a very similar energy profile for QM region M4 (MAD of 1.7 kcal/mol), contrary to the situation for M3a where we had previously found significant discrepancies between the QM‐only and QM/MM results (MAD of 7.9 kcal/mol). Extension of the QM region beyond M4 up to M7 (657 atoms) leads to only rather small variations in the relative energies from single‐point QM‐only and QM/MM calculations (MAD typically about 1–2 kcal/mol). In the case of acetylene hydratase, a model with 408 QM atoms thus seems sufficient to achieve convergence in the computed relative energies to within 1–2 kcal/mol.Copyright © 2013 Wiley Periodicals, Inc.     

QM/MM-PBSA method to estimate free energies for reactions in proteins

We have developed a method to estimate free energies of reactions in proteins, called QM/MM-PBSA. It estimates the internal energy of the reactive site by quantum mechanical (QM) calculations, whereas bonded, electrostatic, and van der Waals interactions with the surrounding protein are calculated at the molecular mechanics (MM) level. The electrostatic part of the solvation energy of the reactant and the product is estimated by solving the Poisson-Boltzmann (PB) equation, and the nonpolar part of the solvation energy is estimated from the change in solvent-accessible surface area (SA). Finally, the change in entropy is estimated from the vibrational frequencies. We test this method for five proton-transfer reactions in the active sites of [Ni,Fe] hydrogenase and copper nitrite reductase. We show that QM/MM-PBSA reproduces the results of a strict QM/MM free-energy perturbation method with a mean absolute deviation (MAD) of 8-10 kJ/mol if snapshots from molecular dynamics simulations are used and 4-14 kJ/mol if a single QM/MM structure is used. This is appreciably better than the original QM/MM results or if the QM energies are supplemented with a point-charge model, a self-consistent reaction field, or a PB model of the protein and the solvent, which give MADs of 22-36 kJ/mol for the same test set.     

QM/MM study of aqueous solvation of the uranyl fluoride [UO2F4(2-)] complex

The aqueous solvation of the uranylfluoride complex [UO(2)F(4) (2-)] was studied using full quantum mechanical (QM) and hybrid QM/molecular mechanics (MM) methods. Inclusion of a complete first solvation shell was found necessary to reproduce the experimentally observed heptacoordination of uranium. An efficient and accurate computational model is proposed that consists of structure optimization of the coordinated uranium complex as QM region, followed by single-point full QM calculations to compute relative energies. This method is proven feasible for studies of large solvated actinide complexes.     

The origins of femtomolar protein-ligand binding: hydrogen-bond cooperativity and desolvation energetics in the biotin-(strept)avidin binding site

The unusually strong reversible binding of biotin by avidin and streptavidin has been investigated by density functional and MP2 ab initio quantum mechanical methods. The solvation of biotin by water has also been studied through QM/MM/MC calculations. The ureido moiety of biotin in the bound state hydrogen bonds to five residues, three to the carbonyl oxygen and one for each--NH group. These five hydrogen bonds act cooperatively, leading to stabilization that is larger than the sum of individual hydrogen-bonding energies. The charged aspartate is the key residue that provides the driving force for cooperativity in the hydrogen-bonding network for both avidin and streptavidin by greatly polarizing the urea of biotin. If the residue is removed, the network is disrupted, and the attenuation of the energetic contributions from the neighboring residues results in significant reduction of cooperative interactions. Aspartate is directly hydrogen-bonded with biotin in streptavidin and is one residue removed in avidin. The hydrogen-bonding groups in streptavidin are computed to give larger cooperative hydrogen-bonding effects than avidin. However, the net gain in electrostatic binding energy is predicted to favor the avidin-bicyclic urea complex due to the relatively large penalty for desolvation of the streptavidin binding site (specifically expulsion of bound water molecules). QM/MM/MC calculations involving biotin and the ureido moiety in aqueous solution, featuring PDDG/PM3, show that water interactions with the bicyclic urea are much weaker than (strept)avidin interactions due to relatively low polarization of the urea group in water.     

Modelling zwitterions in solution: 3-fluoro-γ-aminobutyric acid (3F-GABA)

The conformations and relative stabilities of folded and extended 3-fluoro-γ-aminobutyric acid (3F-GABA) conformers were studied using explicit solvation models. Geometry optimisations in the gas phase with one or two explicit water molecules favour folded and neutral structures containing intramolecular NH···O-C hydrogen bonds. With three or five explicit water molecules zwitterionic minima are obtained, with folded structures being preferred over extended conformers. The stability of folded versus extended zwitterionic conformers increases on going from a PCM continuum solvation model to the microsolvated complexes, though extended structures become less disfavoured with the inclusion of more water molecules. Full explicit solvation was studied with a hybrid quantum-mechanical/molecular-mechanical (QM/MM) scheme and molecular dynamics simulations, including more than 6000 TIP3P water molecules. According to free energies obtained from thermodynamic integration at the PM3/MM level and corrected for B3LYP/MM total energies, the fully extended conformer is more stable than folded ones by about -4.5 kJ mol(-1). B3LYP-computed (3)J(F,H) NMR spin-spin coupling constants, averaged over PM3/MM-MD trajectories, agree best with experiment for this fully extended form, in accordance with the original NMR analysis. The seeming discrepancy between static PCM calculations and experiment noted previously is now resolved. That the inexpensive semiempirical PM3 method performs so well for this archetypical zwitterion is encouraging for further QM/MM studies of biomolecular systems.     

LICHEM: A QM/MM program for simulations with multipolar and polarizable force fields

We introduce an initial implementation of the LICHEM software package. LICHEM can interface with Gaussian, PSI4, NWChem, TINKER, and TINKER–HP to enable QM/MM calculations using multipolar/polarizable force fields. LICHEM extracts forces and energies from unmodified QM and MM software packages to perform geometry optimizations, single‐point energy calculations, or Monte Carlo simulations. When the QM and MM regions are connected by covalent bonds, the pseudo‐bond approach is employed to smoothly transition between the QM region and the polarizable force field. A series of water clusters and small peptides have been employed to test our initial implementation. The results obtained from these test systems show the capabilities of the new software and highlight the importance of including explicit polarization. © 2016 Wiley Periodicals, Inc.     

Binding free energies in the SAMPL6 octa-acid host–guest challenge calculated with MM and QM methods

We have estimated free energies for the binding of eight carboxylate ligands to two variants of the octa-acid deep-cavity host in the SAMPL6 blind-test challenge (with or without endo methyl groups on the four upper-rim benzoate groups, OAM and OAH, respectively). We employed free-energy perturbation (FEP) for relative binding energies at the molecular mechanics (MM) and the combined quantum mechanical (QM) and MM (QM/MM) levels, the latter obtained with the reference-potential approach with QM/MM sampling for the MM → QM/MM FEP. The semiempirical QM method PM6-DH+ was employed for the ligand in the latter calculations. Moreover, binding free energies were also estimated from QM/MM optimised structures, combined with COSMO-RS estimates of the solvation energy and thermostatistical corrections from MM frequencies. They were performed at the PM6-DH+ level of theory with the full host and guest molecule in the QM system (and also four water molecules in the geometry optimisations) for 10–20 snapshots from molecular dynamics simulations of the complex. Finally, the structure with the lowest free energy was recalculated using the dispersion-corrected density-functional theory method TPSS-D3, for both the structure and the energy. The two FEP approaches gave similar results (PM6-DH+/MM slightly better for OAM), which were among the five submissions with the best performance in the challenge and gave the best results without any fit to data from the SAMPL5 challenge, with mean absolute deviations (MAD) of 2.4–5.2 kJ/mol and a correlation coefficient (R²) of 0.77–0.93. This is the first time QM/MM approaches give binding free energies that are competitive to those obtained with MM for the octa-acid host. The QM/MM-optimised structures gave somewhat worse performance (MAD?=?3–8 kJ/mol and R²?=?0.1–0.9), but the results were improved compared to previous studies of this system with similar methods.     

A free-energy perturbation method based on Monte Carlo simulations using quantum mechanical calculations (QM/MC/FEP method): application to highly solvent-dependent reactions

This study describes the framework of the quantum mechanical (QM)/Monte Carlo (MC)/free‐energy perturbation (FEP) method, a FEP method based on MC simulations using quantum chemical calculations. Because a series of structures generated by interpolating internal coordinates between transition state and reactant did not produce smooth free‐energy profiles, we used structures from the intrinsic reaction coordinate calculations. This method was first applied to the Diels–Alder reaction between methyl vinyl ketone and cyclopentadiene and produced ΔG values of 20.1 and 21.4 kcal mol^?1 in aqueous and methanol solutions, respectively. They are very consistent with the experimentally observed values. The other two applications were the free‐energy surfaces for the Cope elimination of N,N‐dimethyl‐3‐phenylbutan‐2‐amine oxide in aqueous, dimethyl sulfoxide, and tetrahydrofuran solutions, and the Kemp decarboxylation of 6‐hydroxybenzo‐isoxazole‐3‐carboxylic acid in aqueous, dimethyl sulfoxide, and CH₃CN solutions. The calculated activation free energies differed by less than 1.8 kcal mol^?1 from the experimental values for these reactions. Although we used droplet models for the QM/MC/FEP simulations, the calculated results for three reactions are very close to the experimental data. It was confirmed that most of the interactions between the solute and solvents can be described using small numbers of solvent molecules. This is because a few solvent molecules can produce large portions of the solute–solvent interaction energies at the reaction centers. When we confirmed the dependency on the droplet sizes of solvents, the QM/MC/FEP for a large droplet with 106 water molecules produced a ΔG value similar to the experimental values, as well as that for a small droplet with 34 molecules. © 2010 Wiley Periodicals, Inc. J Comput Chem, 2011     

Predicting hydration free energies with a hybrid QM/MM approach: an evaluation of implicit and explicit solvation models in SAMPL4

The correct representation of solute-water interactions is essential for the accurate simulation of most biological phenomena. Several highly accurate quantum methods are available to deal with solvation by using both implicit and explicit solvents. So far, however, most evaluations of those methods were based on a single conformation, which neglects solute entropy. Here, we present the first test of a novel approach to determine hydration free energies that uses molecular mechanics (MM) to sample phase space and quantum mechanics (QM) to evaluate the potential energies. Free energies are determined by using re-weighting with the Non-Boltzmann Bennett (NBB) method. In this context, the method is referred to as QM-NBB. Based on snapshots from MM sampling and accounting for their correct Boltzmann weight, it is possible to obtain hydration free energies that incorporate the effect of solute entropy. We evaluate the performance of several QM implicit solvent models, as well as explicit solvent QM/MM for the blind subset of the SAMPL4 hydration free energy challenge. While classical free energy simulations with molecular dynamics give root mean square deviations (RMSD) of 2.8 and 2.3 kcal/mol, the hybrid approach yields an improved RMSD of 1.6 kcal/mol. By selecting an appropriate functional and basis set, the RMSD can be reduced to 1 kcal/mol for calculations based on a single conformation. Results for a selected set of challenging molecules imply that this RMSD can be further reduced by using NBB to reweight MM trajectories with the SMD implicit solvent model.     

A QM/MM study of the binding of RAPTA ligands to cathepsin B

We have carried out quantum mechanical (QM) and QM/MM (combined QM and molecular mechanics) calculations, as well as molecular dynamics (MD) simulations to study the binding of a series of six RAPTA (Ru(II)-arene-1,3,5-triaza-7-phosphatricyclo-[3.3.1.1] decane) complexes with different arene substituents to cathepsin B. The recently developed QM/MM-PBSA approach (QM/MM combined with Poisson–Boltzmann solvent-accessible surface area solvation) has been used to estimate binding affinities. The QM calculations reproduce the antitumour activities of the complexes with a correlation coefficient (r ²) of 0.35–0.86 after a conformational search. The QM/MM-PBSA method gave a better correlation (r ² = 0.59) when the protein was fixed to the crystal structure, but more reasonable ligand structures and absolute binding energies were obtained if the protein was allowed to relax, indicating that the ligands are strained when the protein is kept fixed. In addition, the best correlation (r ² = 0.80) was obtained when only the QM energies were used, which suggests that the MM and continuum solvation energies are not accurate enough to predict the binding of a charged metal complex to a charged protein. Taking into account the protein flexibility by means of MD simulations slightly improves the correlation (r ² = 0.91), but the absolute energies are still too large and the results are sensitive to the details in the calculations, illustrating that it is hard to obtain stable predictions when full flexible protein is included in the calculations.     

The role of local structure on formic acid decomposition in supercritical water: A hybrid quantum mechanics/Monte Carlo study

We explored water-assisted decompositions of formic acid in supercritical water in terms of local structure near reactant. A hybrid quantum mechanics/molecular mechanics (QM/MM) simulation used in this paper includes QM part as first solvation shell members around the reactant. A present QM/MM approach can simulate supercritical water solution with a reasonable computational load while keeping the simulation preciseness because a density functional theory of B3LYP/6-31+G(d) level was iterated at every 1000 Monte Carlo solute moves. The formic acid converts mainly decarboxylation by water-assisted mechanism, and the coordinated water molecules play an important role for understanding supercritical water density dependence of the reaction. We analyzed a contour map based on the solute–solvent interaction energy along with the reaction pathway. Coordinated water molecule restricted the dehydration pathway by means of hydrogen bond with formic acid, however, the coordinated water promotes the decarboxylation pathway by means of stabilization of the transition state structure with one catalytic water molecule. The contour map of the pair interaction energy along the reaction path elucidates the role of local structure on reactions in supercritical water.     

Contributions of conformational compression and preferential transition state stabilization to the rate enhancement by chorismate mutase

The rate enhancement provided by the chorismate mutase (CM) enzyme for the Claisen rearrangement of chorismate to prephenate has been investigated by application of the concept of near attack conformations (NACs). Using a combined QM/MM Monte Carlo/free-energy perturbation (MC/FEP) method, 82% and 100% of chorismate conformers were found to be NAC structures in water and in the CM active site, respectively. Consequently, the conversion of non-NACs to NACs does not contribute to the free energy of activation from preorganization of the substrate into NACs. The FEP calculations yielded differences in free energies of activation that well reproduce the experimental data. Additional calculations indicate that the rate enhancement by CM over the aqueous phase results primarily from conformational compression of NACs by the enzyme and that this process is enthalpically controlled. This suggests that preferential stabilization of the transition state in the enzyme environment relative to water plays a secondary role in the catalysis by CM.     

Combined QM/MM study of the mechanism and kinetic isotope effect of the nucleophilic substitution reaction in haloalkane dehalogenase

Combined QM/MM molecular dynamics simulations have been carried out for the dehalogenation reaction of the nucleophilic displacement of dichloroethane catalyzed by haloalkane dehalogenase. The computed chlorine kinetic isotope effects and free energies of activation in the wild-type and the Phe172Trp mutant enzyme are found to be consistent with experiment. In comparison with the uncatalyzed model reaction in water, the enzyme lowers the activation barrier by about 16 kcal/mol. The enormous enzymatic action was attributed to a combination of contributions from a change in the solvation effect and transition state stabilization. The unique features of tryptophan's ability to interact favorably with hydrophobic substrates and to form hydrogen bonds to the leaving group chloride ion at the transition state enable both factors to make significant contributions to the barrier lowering mechanism in the enzyme. This is in contrast to the reference reaction in water, in which hydrogen bonding interactions are weakened at the transition state because of dispersed charge distribution at the transition state relative to that in the reactant and product states.