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.     

The adaptive buffered force QM/MM method in the CP2K and AMBER software packages

The implementation and validation of the adaptive buffered force (AdBF) quantum‐mechanics/molecular‐mechanics (QM/MM) method in two popular packages, CP2K and AMBER are presented. The implementations build on the existing QM/MM functionality in each code, extending it to allow for redefinition of the QM and MM regions during the simulation and reducing QM‐MM interface errors by discarding forces near the boundary according to the buffered force‐mixing approach. New adaptive thermostats, needed by force‐mixing methods, are also implemented. Different variants of the method are benchmarked by simulating the structure of bulk water, water autoprotolysis in the presence of zinc and dimethyl‐phosphate hydrolysis using various semiempirical Hamiltonians and density functional theory as the QM model. It is shown that with suitable parameters, based on force convergence tests, the AdBF QM/MM scheme can provide an accurate approximation of the structure in the dynamical QM region matching the corresponding fully QM simulations, as well as reproducing the correct energetics in all cases. Adaptive unbuffered force‐mixing and adaptive conventional QM/MM methods also provide reasonable results for some systems, but are more likely to suffer from instabilities and inaccuracies. © 2015 The Authors. Journal of Computational Chemistry Published by Wiley Periodicals, Inc.     

Why urea eliminates ammonia rather than hydrolyzes in aqueous solution

A joint QM/MM and ab initio study on the decomposition of urea in the gas phase and in aqueous solution is reported. Numerous possible mechanisms of intramolecular decomposition and hydrolysis have been explored; intramolecular NH3 elimination assisted by a water molecule is found to have the lowest activation energy. The solvent effects were elucidated using the TIP4P explicit water model with free energy perturbation calculations in conjunction with QM/MM Monte Carlo simulations. The explicit representation of the solvent was found to be essential for detailed resolution of the mechanism, identification of the rate-determining step, and evaluation of the barrier. The assisting water molecule acts as a hydrogen shuttle for the first step of the elimination reaction. The forming zwitterionic intermediate, H3NCONH, participates in 8-9 hydrogen bonds with water molecules. Its decomposition is found to be the rate-limiting step, and the overall free energy of activation for the decomposition of urea in water is computed to be approximately 37 kcal/mol; the barrier for hydrolysis by an addition/elimination mechanism is found to be approximately 40 kcal/mol. The differences in the electronic structure of the transition states of the NH3 elimination and hydrolysis were examined via natural bond order analysis. Destruction of urea's resonance stabilization during hydrolysis via an addition/elimination mechanism and its preservation in the rearrangement to the H3NCONH intermediate were identified as important factors in determining the preferred reaction route.     

Mixed ab initio QM/MM modeling using frozen orbitals and tests with alanine dipeptide and tetrapeptide

Methodology is discussed for mixed ab initio quantum mechanics/molecular mechanics modeling of systems where the quantum mechanics (QM) and molecular mechanics (MM) regions are within the same molecule. The ab initio QM calculations are at the restricted Hartree–Fock level using the pseudospectral method of the Jaguar program while the MM part is treated with the OPLS force fields implemented in the IMPACT program. The interface between the QM and MM regions, in particular, is elaborated upon, as it is dealt with by “breaking” bonds at the boundaries and using Boys-localized orbitals found from model molecules in place of the bonds. These orbitals are kept frozen during QM calculations. Results from tests of the method to find relative conformational energies and geometries of alanine dipeptides and alanine tetrapeptides are presented along with comparisons to pure QM and pure MM calculations. ©1999 John Wiley & Sons, Inc. J Comput Chem 20: 1468–1494, 1999     

Water solvent effects using continuum and discrete models: The nitromethane molecule,CH3NO2

The first three valence transitions of the two nitromethane conformers (CH₃NO₂) are two dark n → π* transitions and a very intense π → π* transition. In this work, these transitions in gas‐phase and solvated in water of both conformers were investigated theoretically. The polarizable continuum model (PCM), two conductor‐like screening (COSMO) models, and the discrete sequential quantum mechanics/molecular mechanics (S‐QM/MM) method were used to describe the solvation effect on the electronic spectra. Time dependent density functional theory (TDDFT), configuration interaction including all single substitutions and perturbed double excitations (CIS(D)), the symmetry‐adapted‐cluster CI (SAC‐CI), the multistate complete active space second order perturbation theory (CASPT2), and the algebraic‐diagrammatic construction (ADC(2)) electronic structure methods were used. Gas‐phase CASPT2, SAC‐CI, and ADC(2) results are in very good agreement with published experimental and theoretical spectra. Among the continuum models, PCM combined either with CASPT2, SAC‐CI, or B3LYP provided good agreement with available experimental data. COSMO combined with ADC(2) described the overall trends of the transition energy shifts. The effect of increasing the number of explicit water molecules in the S‐QM/MM approach was discussed and the formation of hydrogen bonds was clearly established. By including explicitly 24 water molecules corresponding to the complete first solvation shell in the S‐QM/MM approach, the ADC(2) method gives more accurate results as compared to the TDDFT approach and with similar computational demands. The ADC(2) with S‐QM/MM model is, therefore, the best compromise for accurate solvent calculations in a polar environment. © 2015 Wiley Periodicals, Inc.     

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.     

Density functional self-consistent quantum mechanics/molecular mechanics theory for linear and nonlinear molecular properties: Applications to solvated water and formaldehyde

A combined quantum mechanics/molecular mechanics (QM/MM) method is described, where the polarization between the solvent and solute is accounted for using a self-consistent scheme linear in the solvent polarization. The QM/MM method is implemented for calculation of energies and molecular response properties including the calculation of linear and quadratic response functions using the density-functional theory (DFT) and the Hartree-Fock (HF) theory. Sample calculations presented for ground-state energies, first-order ground-state properties, excitation energies, first-order excited state properties, polarizabilities, first-hyperpolarizabilities, and two-photon absorptions strengths of formaldehyde suggests that DFT may in some cases be a sufficiently reliable alternative to high-level theory, such as coupled-cluster (CC) theory, in modeling solvent shifts, whereas results obtained with the HF wave function deviate significantly from the CC results. Calculations carried out on water gives results that also are comparable with CC calculations in accuracy for ground-state and first-order properties. However, to obtain such accuracy an exchange-correlation functional capable of describing the diffuse Rydberg states must be chosen.     

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.     

Structure of the enzyme-substrate complex for guanosine triphosphate hydrolysis by elongation factor EF-Tu: Comparison of quantum mechanics/molecular mechanics and molecular dynamics results

The equilibrium geometric configurations of the enzyme-substrate complex for guanosine triphosphate hydrolysis by elongation factor EF-Tu calculated using two theoretical approaches, a combined quantum mechanics/molecular mechanics (QM/MM) method and a molecular dynamics method, are compared. The reaction complex geometry determined by the QM/MM method is consistent with the accepted reaction mechanism, whereas, in the enzyme-substrate structure predicted by the molecular dynamics method with the CHARMM force field, the relative positions of the nucleophilic reagent (water molecules) and the base (a histidine side chain) do not correspond to the optimal reagent arrangement.     

Structural and spectroscopic properties of the peroxodiferric intermediate of Ricinus communis soluble Δ9 desaturase

Large-scale quantum and molecular mechanical methods (QM/MM) and QM calculations were carried out on the soluble Δ(9) desaturase (Δ(9)D) to investigate various structural models of the spectroscopically defined peroxodiferric (P) intermediate. This allowed us to formulate a consistent mechanistic picture for the initial stages of the reaction mechanism of Δ(9)D, an important diferrous nonheme iron enzyme that cleaves the C-H bonds in alkane chains resulting in the highly specific insertion of double bonds. The methods (density functional theory (DFT), time-dependent DFT (TD-DFT), QM(DFT)/MM, and TD-DFT with electrostatic embedding) were benchmarked by demonstrating that the known spectroscopic effects and structural perturbation caused by substrate binding to diferrous Δ(9)D can be qualitatively reproduced. We show that structural models whose spectroscopic (absorption, circular dichroism (CD), vibrational and M?ssbauer) characteristics correlate best with experimental data for the P intermediate correspond to the μ-1,2-O(2)(2-) binding mode. Coordination of Glu196 to one of the iron centers (Fe(B)) is demonstrated to be flexible, with the monodentate binding providing better agreement with spectroscopic data, and the bidentate structure being slightly favored energetically (1-10 kJ mol(-1)). Further possible structures, containing an additional proton or water molecule are also evaluated in connection with the possible activation of the P intermediate. Specifically, we suggest that protonation of the peroxide moiety, possibly preceded by water binding in the Fe(A) coordination sphere, could be responsible for the conversion of the P intermediate in Δ(9)D into a form capable of hydrogen abstraction. Finally, results are compared with recent findings on the related ribonucleotide reductase and toluene/methane monooxygenase enzymes.     

Assessing the validity of DLPNO-CCSD(T) in the calculation of activation and reaction energies of ubiquitous enzymatic reactions

The domain-based local pair natural orbital coupled-cluster with single, double, and perturbative triples excitation (DLPNO-CCSD(T)) method was employed to portray the activation and reaction energies of four ubiquitous enzymatic reactions, and its performance was confronted to CCSD(T)/complete basis set (CBS) to assess its accuracy and robustness in this specific field. The DLPNO-CCSD(T) results were also confronted to those of a set of density functionals (DFs) to understand the benefit of implementing this technique in enzymatic quantum mechanics/molecular mechanics (QM/MM) calculations as a second QM component, which is often treated with DF theory (DFT). On average, the DLPNO-CCSD(T)/aug-cc-pVTZ results were 0.51 kcal·mol⁻¹ apart from the canonic CCSD(T)/CBS, without noticeable biases toward any of the reactions under study. All DFs fell short to the DLPNO-CCSD(T), both in terms of accuracy and robustness, which suggests that this method is advantageous to characterize enzymatic reactions and that its use in QM/MM calculations, either alone or in conjugation with DFT, in a two-region QM layer (DLPNO-CCSD(T):DFT), should enhance the quality and faithfulness of the results.     

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.     

Is inhibition process better described with MD(QM/MM) simulations? The case of urokinase type plasminogen activator inhibitors

Urokinase plasminogen activator (uPA) is an enzyme involved in cancer growth and metastasis. Therefore, the design of inhibitors of uPA is of high therapeutic value, and several chemical families have been explored, even if none has still emerged, emphasizing the need of a rationalized approach. This work represents a complete computational study of uPA complexed with five inhibitors, which present weak similarities. Molecular dynamics simulations in explicit solvent were conducted, and structural analyses, along with molecular mechanics (MM)/Poisson-Boltzmann surface area free energies estimations, yield precious structure-activity relationships of these inhibitors. Besides, we realized supplemental QM/MM computations that improved drastically the quality of our models providing original information on the hydrogen bonds and charge transfer effects, which are, most often, neglected in other studies. We suggest that these simulations and analyses could be reproduced for other systems involving protein/ligand molecular recognitions.     

Implementation of the IMOMM methodology for performing combined QM/MM molecular dynamics simulations and frequency calculations

A technique for implementing the integrated molecular orbital and molecular mechanics (IMOMM) methodology developed by Maseras and Morokuma that is used to perform combined quantum mechanics/molecular mechanics (QM/MM) molecular dynamics simulations, frequency calculations and simulations of macromolecules including explicit solvent is presented. Although the IMOMM methodology is generalized to any coordinate system, the implementation first described by Maseras and Morokuma requires that the QM and MM gradients be transformed into internal coordinates before they are added together. This coordinate transformation can be cumbersome for macromolecular systems and can become ill-defined during the course of a molecular dynamics simulation. We describe an implementation of the IMOMM method in which the QM and MM gradients are combined in the cartesian coordinate system, thereby avoiding potential problems associated with using the internal coordinate system. The implementation can be used to perform combined QM/MM molecular dynamics simulations and frequency calculations within the IMOMM framework. Finally, we have examined the applicability of thermochemical data derived from IMOMM framework. Finally, we have examined the applicability of thermochemical data derived from IMOMM frequency calculations. Received: 11 May 1998 / Accepted: 14 August 1998 / Published online: 16 November 1998     

Cope elimination: elucidation of solvent effects from QM/MM simulations

The Cope elimination reactions for threo- and erythro-N,N-dimethyl-3-phenyl-2-butylamine oxide have been investigated using QM/MM calculations in water, THF, and DMSO. The aprotic solvents provide up to million-fold rate accelerations. The effects of solvation on the reactants, transition structures, and rates of reaction are elucidated here using two-dimensional potentials of mean force (PMF) derived from free-energy perturbation calculations in Monte Carlo simulations (MC/FEP). The resultant free energies of activation in solution are in close agreement with experiment. Ab initio calculations at the MP2/6-311+G-(2d,p) level using the PCM continuum solvent model were also carried out; however, only the QM/MM methodology was able to reproduce the large rate increases in proceeding from water to the dipolar aprotic solvents. Solute-solvent interaction energies and radial distribution functions are also analyzed and show that poorer solvation of the reactant in the aprotic solvents is primarily responsible for the observed rate enhancements. It is found that the amine oxide oxygen is the acceptor of three hydrogen bonds from water molecules for the reactant but only one to two weaker ones at the transition state. The overall quantitative success of the computations supports the present QM/MM/MC approach, featuring PDDG/PM3 as the QM method.     

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.     

De novo prediction of the ground state structure of transition metal complexes using semiempirical and ab initio quantum mechanics. Coordination isomerism

The ground state coordination isomers for 30 different trigonal bipyramidal transition metal complexes have been predicted using different levels of quantum mechanics: semiempirical (PM3(tm)), ab initio (MP2//HF), pure (BPW91) and hybrid (B3PW91) density functional theory (DFT) methods. For species where these methods failed to reproduce crystallographic data, hybrid quantum mechanics/molecular mechanics (QM/MM) methods were used to study more exact experimental models. Literature deficiencies regarding ground state multiplicity of these species were supplemented by spin predictions using previously tested PM3(tm) methods. Geometry optimization calculations were performed for each possible coordination isomer. The predicted ground state minima provided by the different methods are compared to each other and with crystallographic data. Pure DFT functionals outperformed hybrid functionals and MP2//HF. The very rapid PM3(tm) parameterization method provided accurate predictions in comparison to other levels of theory. An integrated MM/PM3(tm)/DFT de novo scheme accurately reproduced crystallographic data for species where the individual methods failed.