Toward accurate barriers for enzymatic reactions: QM/MM case study on p-hydroxybenzoate hydroxylase

The hydroxylation reaction catalyzed by p-hydroxybenzoate hydroxylase has been investigated by quantum mechanical/molecular mechanical (QM/MM) calculations at different levels of QM theory. The solvated enzyme was modeled (approximately 23,000 atoms in total, 49 QM atoms). The geometries of reactant and transition state were optimized for ten representative pathways using semiempirical (AM1) and density functional (B3LYP) methods as QM components. Single-point calculations at B3LYP/MM optimized geometries were performed with local correlation methods [LMP2, LCCSD(T0)] and augmented triple-zeta basis sets. A careful validation of the latter approach with regard to all computational parameters indicates convergence of the QM contribution to the computed barriers to within approximately 1 kcal mol(-1). Comparison with the available experimental data supports this assessment.     

Importance of selecting proper basis set in quantum mechanical studies of potential energy surfaces of carbohydrates

An extensive quantum mechanical study of a water dimer suggests that the introduction of a diffuse function into the basis set, which significantly reduces the basis set superposition error (BSSE) in the hydrogen bonding energy calculation, is the key to better calculations of the potential energy surfaces of carbohydrates. This article examines the potential energy surfaces of selected d -aldo- and d -ketohexoses (a total of 82 conformers) by quantum mechanics (QM) and molecular mechanics (MM) methods. In contrast to the results with a smaller basis set (B3LYP/6-31G** 5d), we found at the higher level calculation (B3LYP/6-311++G(2d,2p)//B3LYP/6-31G** 5d) that, in most cases, the furanose forms are less stable than the pyranose forms. These discrepancies are mainly due to the fact that intramolecular hydrogen bonding energies are overestimated in the lower level calculations. The higher level QM calculations of the potential energy surfaces of d -aldo- and d -ketohexoses now are more comparable to the MM3 results. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1593–1603, 1999     

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.     

A comparative study of various computational approaches in calculating the structure of pyridoxal 5'-phosphate (PLP)-dependent beta-lyase protein. The importance of protein environment

Various computational approaches, using molecular mechanics (Amber), semiempirical (AM1), density functional (B3LYP), and various ONIOM methods, have been comparatively investigated for the structure of Escherichia coli NifS CsdB protein. The structure of the entire monomer containing 407 amino acid residues and 579 surrounding water molecules has been optimized. The full geometry optimization in the "active site-only" approach (including only active site atoms) has been found to give the largest root-mean-square (RMS) deviation from the X-ray structure; a much better agreement has been achieved by keeping the atoms leading to the backbones of some amino acids frozen in their positions in the X-ray structure. The best agreement has been attained by including the surrounding protein in the calculations using the two-layer ONIOM (B3LYP:Amber) approach. The results presented in this study conclusively demonstrate the importance of the protein/active-site interaction on the active-site structure of the enzyme. The present theoretical study represents the largest system studied at the ONIOM level to date, containing 7992 atoms, including 84 atoms in the QM region and rest in the MM region.     

A combined quantum chemical/molecular mechanical study of hydrogen-bonded systems

A computational approach, which involves the combination of the OPLS force field and molecular orbital MNDO , AM 1, and PM 3 methods, has been developed to describe the effects of a large, molecular mechanically simulated environment on the Hamiltonian of a quantum chemical system. To test the validity of the combined quantum mechanical/molecular mechanical (QM /MM ) potential, a systematic study of the structures and energies of neutral and charged hydrogen-bonded complexes has been carried out, including comparisons with pure semiempirical calculations and available experimental and ab initio data. It is shown that, in many cases, the hybrid QM /MM potential behaves better than do related MNDO /M , AM 1, and PM 3 methods. As a case in point, the draw-back of AM 1 favoring bifurcated H-bonded structures over single ones is not presented in the combined AM 1/OPLS scheme. Possible ways of improvement of the combined QM /MM potential are discussed. © 1992 John Wiley & Sons, Inc.     

Mechanism of proteolysis in matrix metalloproteinase‐2 revealed by QM/MM modeling

The mechanism of enzymatic peptide hydrolysis in matrix metalloproteinase‐2 (MMP‐2) was studied at atomic resolution through quantum mechanics/molecular mechanics (QM/MM) simulations. An all‐atom three‐dimensional molecular model was constructed on the basis of a crystal structure from the Protein Data Bank (ID: 1QIB), and the oligopeptide Ace‐Gln‐Gly～Ile‐Ala‐Gly‐Nme was considered as the substrate. Two QM/MM software packages and several computational protocols were employed to calculate QM/MM energy profiles for a four‐step mechanism involving an initial nucleophilic attack followed by hydrogen bond rearrangement, proton transfer, and C? N bond cleavage. These QM/MM calculations consistently yield rather low overall barriers for the chemical steps, in the range of 5–10 kcal/mol, for diverse QM treatments (PBE0, B3LYP, and BB1K density functionals as well as local coupled cluster treatments) and two MM force fields (CHARMM and AMBER). It, thus, seems likely that product release is the rate‐limiting step in MMP‐2 catalysis. This is supported by an exploration of various release channels through QM/MM reaction path calculations and steered molecular dynamics simulations. © 2015 Wiley Periodicals, Inc.     

Quantum mechanical/molecular mechanical study on the mechanism of the enzymatic Baeyer-Villiger reaction

We report a combined quantum mechanical/molecular mechanical (QM/MM) study on the mechanism of the enzymatic Baeyer-Villiger reaction catalyzed by cyclohexanone monooxygenase (CHMO). In QM/MM geometry optimizations and reaction path calculations, density functional theory (B3LYP/TZVP) is used to describe the QM region consisting of the substrate (cyclohexanone), the isoalloxazine ring of C4a-peroxyflavin, the side chain of Arg-329, and the nicotinamide ring and the adjacent ribose of NADP(+), while the remainder of the enzyme is represented by the CHARMM force field. QM/MM molecular dynamics simulations and free energy calculations at the semiempirical OM3/CHARMM level employ the same QM/MM partitioning. According to the QM/MM calculations, the enzyme-reactant complex contains an anionic deprotonated C4a-peroxyflavin that is stabilized by strong hydrogen bonds with the Arg-329 residue and the NADP(+) cofactor. The CHMO-catalyzed reaction proceeds via a Criegee intermediate having pronounced anionic character. The initial addition reaction has to overcome an energy barrier of about 9 kcal/mol. The formed Criegee intermediate occupies a shallow minimum on the QM/MM potential energy surface and can undergo fragmentation to the lactone product by surmounting a second energy barrier of about 7 kcal/mol. The transition state for the latter migration step is the highest point on the QM/MM energy profile. Gas-phase reoptimizations of the QM region lead to higher barriers and confirm the crucial role of the Arg-329 residue and the NADP(+) cofactor for the catalytic efficiency of CHMO. QM/MM calculations for the CHMO-catalyzed oxidation of 4-methylcyclohexanone reproduce and rationalize the experimentally observed (S)-enantioselectivity for this substrate, which is governed by the conformational preferences of the corresponding Criegee intermediate and the subsequent transition state for the migration step.     

OMx-D: semiempirical methods with orthogonalization and dispersion corrections. Implementation and biochemical application

The semiempirical methods of the OMx family (orthogonalization models OM1, OM2, and OM3) are known to describe biochemical systems more accurately than standard semiempirical approaches such as AM1. We investigate the benefits of augmenting these methods with an empirical dispersion term (OMx-D) taken from recent density functional work, without modifying the standard OMx parameters. Significant improvements are achieved for non-covalent interactions, with mean unsigned errors of 1.41 kcal/mol (OM2-D) and 1.31 kcal/mol (OM3-D) for the binding energy of the complexes in the JSCH-2005 data base. This supports the use of these augmented methods in quantum mechanical/molecular mechanical (QM/MM) studies of biomolecules, for example during system preparation and equilibration. As an illustrative application, we present QM and QM/MM calculations on the binding between antibody 34E4 and a hapten, where OM3-D performs better than the methods without dispersion terms (AM1, OM3).     

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.     

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     

Theoretical study of vitamin properties from combined QM-MM methods: Comparison of chemical shifts and energy

The combination of quantum mechanics (QM) and molecular mechanics (MM) methods has become an alternative tool for many applications for which pure QM and MM are not suitable. The QM-MM method has been used for different types of problems, for example, structural biology, surface phenomena, and the liquid phase. In this paper, we have implemented these methods for vitamins, an important kind of biological molecule, and then compared results. The calculations were done by the full ab initio method (HF/3–21 g and HF/6–31 g) and QM-MM (ONIOM) method with HF(3–21 g)/AM1/UFF; then, we found that the geometry obtained by the QM-MM method is very accurate and this rapid method can be used in place of time consuming ab initio methods for large molecules. A comparison of energy values in the QM-MM and QM methods is given. We compare chemical shifts and conclude that the QM-MM method is a perturbed full QM method. The text was submitted by the authors in English.     

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.     

Comparison of linear-scaling semiempirical methods and combined quantum mechanical/molecular mechanical methods for enzymic reactions. II. An energy decomposition analysis

QM/MM methods have been developed as a computationally feasible solution to QM simulation of chemical processes, such as enzyme-catalyzed reactions, within a more approximate MM representation of the condensed-phase environment. However, there has been no independent method for checking the quality of this representation, especially for highly nonisotropic protein environments such as those surrounding enzyme active sites. Hence, the validity of QM/MM methods is largely untested. Here we use the possibility of performing all-QM calculations at the semiempirical PM3 level with a linear-scaling method (MOZYME) to assess the performance of a QM/MM method (PM3/AMBER94 force field). Using two model pathways for the hydride-ion transfer reaction of the enzyme dihydrofolate reductase studied previously (Titmuss et al., Chem Phys Lett 2000, 320, 169-176), we have analyzed the reaction energy contributions (QM, QM/MM, and MM) from the QM/MM results and compared them with analogous-region components calculated via an energy partitioning scheme implemented into MOZYME. This analysis further divided the MOZYME components into Coulomb, resonance and exchange energy terms. For the model in which the MM coordinates are kept fixed during the reaction, we find that the MOZYME and QM/MM total energy profiles agree very well, but that there are significant differences in the energy components. Most significantly there is a large change (approximately 16 kcal/mol) in the MOZYME MM component due to polarization of the MM region surrounding the active site, and which arises mostly from MM atoms close to (<10 A) the active-site QM region, which is not modelled explicitly by our QM/MM method. However, for the model where the MM coordinates are allowed to vary during the reaction, we find large differences in the MOZYME and QM/MM total energy profiles, with a discrepancy of 52 kcal/mol between the relative reaction (product-reactant) energies. This is largely due to a difference in the MM energies of 58 kcal/mol, of which we can attribute approximately 40 kcal/mol to geometry effects in the MM region and the remainder, as before, to MM region polarization. Contrary to the fixed-geometry model, there is no correlation of the MM energy changes with distance from the QM region, nor are they contributed by only a few residues. Overall, the results suggest that merely extending the size of the QM region in the QM/MM calculation is not a universal solution to the MOZYME- and QM/MM-method differences. They also suggest that attaching physical significance to MOZYME Coulomb, resonance and exchange components is problematic. Although we conclude that it would be possible to reparameterize the QM/MM force field to reproduce MOZYME energies, a better way to account for both the effects of the protein environment and known deficiencies in semiempirical methods would be to parameterize the force field based on data from DFT or ab initio QM linear-scaling calculations. Such a force field could be used efficiently in MD simulations to calculate free energies.     

Testing electronic structure methods for describing intermolecular H...H interactions in supramolecular chemistry

In this article a wide variety of computational approaches (molecular mechanics force fields, semiempirical formalisms, and hybrid methods, namely ONIOM calculations) have been used to calculate the energy and geometry of the supramolecular system 2-(2'-hydroxyphenyl)-4-methyloxazole (HPMO) encapsulated in beta-cyclodextrin (beta-CD). The main objective of the present study has been to examine the performance of these computational methods when describing the short range H. H intermolecular interactions between guest (HPMO) and host (beta-CD) molecules. The analyzed molecular mechanics methods do not provide unphysical short H...H contacts, but it is obvious that their applicability to the study of supramolecular systems is rather limited. For the semiempirical methods, MNDO is found to generate more reliable geometries than AM1, PM3 and the two recently developed schemes PDDG/MNDO and PDDG/PM3. MNDO results only give one slightly short H...H distance, whereas the NDDO formalisms with modifications of the Core Repulsion Function (CRF) via Gaussians exhibit a large number of short to very short and unphysical H...H intermolecular distances. In contrast, the PM5 method, which is the successor to PM3, gives very promising results. Our ONIOM calculations indicate that the unphysical optimized geometries from PM3 are retained when this semiempirical method is used as the low level layer in a QM:QM formulation. On the other hand, ab initio methods involving good enough basis sets, at least for the high level layer in a hybrid ONIOM calculation, behave well, but they may be too expensive in practice for most supramolecular chemistry applications. Finally, the performance of the evaluated computational methods has also been tested by evaluating the energetic difference between the two most stable conformations of the host(beta-CD)-guest(HPMO) system.     

Tunneling and classical paths for proton transfer in an enzyme reaction dominated by tunneling: oxidation of tryptamine by aromatic amine dehydrogenase

Proton tunneling dominates the oxidative deamination of tryptamine catalyzed by the enzyme aromatic amine dehydrogenase. For reaction with the fast substrate tryptamine, a H/D kinetic isotope effect (KIE) of 55 +/- 6 has been reported-one of the largest observed in an enzyme reaction. We present here a computational analysis of this proton-transfer reaction, applying combined quantum mechanics/molecular mechanics (QM/MM) methods (PM3-SRP//PM3/CHARMM22). In particular, we extend our previous computational study (Masgrau et al. Science 2006, 312, 237) by using improved energy corrections, high-level QM/MM methods, and an ensemble of paths to estimate the tunneling contributions. We have carried out QM/MM molecular dynamics simulations and variational transition state theory calculations with small-curvature tunneling corrections. The results provide detailed insight into the processes involved in the reaction. Transfer to the O2 oxygen of the catalytic base, Asp128beta, is found to be the favored reaction both thermodynamically and kinetically, even though O1 is closer in the reactant complex. Comparison of quantum and classical models of proton transfer allows estimation of the contribution of hydrogen tunneling in lowering the barrier to reaction in the enzyme. A reduction of the activation free energy due to tunneling of 3.1 kcal mol-1 is found, which represents a rate enhancement due to tunneling by 2 orders of magnitude. The calculated KIE of 30 is significantly elevated over the semiclassical limit, in agreement with the experimental observations; a semiclassical value of 6 is obtained when tunneling is omitted. A polarization of the C-H bond to be broken is observed due to the close proximity of the catalytic aspartate and the (formally) positively charged imine nitrogen. A comparison is also made with the related quinoprotein methylamine dehydrogenase (MADH)-the much lower KIE of 11 that we obtain for the MADH/methylamine system is found to arise from a more endothermic potential energy surface for the MADH reaction.     

Probing the range of applicability of structure‐ and energy‐adjusted QM/MM link bonds

The hydrogen‐capping method is one of the most popular and widely used coupling‐schemes for quantum mechanics/molecular mechanics (QM/MM)‐molecular dynamics simulations of macromolecular systems. This is mostly due to the fact that it is fairly convenient to implement and parametrize, thus providing an excellent compromise between accuracy and computational effort. In this work, a viable and straight‐forward approach to optimize the placing of the link atom on a suitable distance ratio between the frontier atoms is discussed. To further increase the accuracy, instead of global parameters for all amino acids, different parameter sets for each type of amino acid are derived. The dependency of the link bond parameters on the chemical environment and the used QM‐method is probed to assess the range of applicability of the parametrization. Suitable sets of parameters for RI‐MP2, B3LYP, (RI)‐B3LYP‐D3, and RI‐BLYP‐D3 at triple‐zeta level for all relevant proteinogenic amino acids are presented. Furthermore, the scope and range of the perturbation, stemming from the introduction of link bonds is evaluated through application of the presented QM/MM scheme in calculations of the active site of 15S‐lipoxygenase. © 2015 Wiley Periodicals, Inc.     

Simulations of liquid ammonia based on the combined quantum mechanical/molecular mechanical (QM/MM) approach

Two combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations, namely, HF/MM and B3LYP/MM, have been performed to investigate the local structure and dynamics of liquid ammonia. The most interesting region, a sphere containing a central reference molecule and all its nearest surrounding molecules (first coordination shell), was treated by the Hartree-Fock (HF) and hybrid density functional B3LYP methods, whereas the rest of the system was described by the classical pair potentials. On the basis of both HF and B3LYP methods, it is observed that the hydrogen bonding in this peculiar liquid is weak. The structure and dynamics of this liquid are suggested to be determined by the steric packing effects, rather than by the directional hydrogen bonding interactions. Compared to previous empirical as well as Car-Parrinello (CP) molecular dynamics studies, our QM/MM simulations provide detailed information that is in better agreement with experimental data.