Two Sides of Quantum-Based Modeling of Enzyme-Catalyzed Reactions: Mechanistic and Electronic Structure Aspects of the Hydrolysis by Glutamate Carboxypeptidase

We report the results of a computational study of the hydrolysis reaction mechanism of N-acetyl-l-aspartyl-l-glutamate (NAAG) catalyzed by glutamate carboxypeptidase II. Analysis of both mechanistic and electronic structure aspects of this multistep reaction is in the focus of this work. In these simulations, model systems are constructed using the relevant crystal structure of the mutated inactive enzyme. After selection of reaction coordinates, the Gibbs energy profiles of elementary steps of the reaction are computed using molecular dynamics simulations with ab initio type QM/MM potentials (QM/MM MD). Energies and forces in the large QM subsystem are estimated in the DFT(PBE0-D3/6-31G**) approximation. The established mechanism includes four elementary steps with the activation energy barriers not exceeding 7 kcal/mol. The models explain the role of point mutations in the enzyme observed in the experimental kinetic studies; namely, the Tyr552Ile substitution disturbs the “oxyanion hole”, and the Glu424Gln replacement increases the distance of the nucleophilic attack. Both issues diminish the substrate activation in the enzyme active site. To quantify the substrate activation, we apply the QTAIM-based approaches and the NBO analysis of dynamic features of the corresponding enzyme-substrate complexes. Analysis of the 2D Laplacian of electron density maps allows one to define structures with the electron density deconcentration on the substrate carbon atom, i.e., at the electrophilic site of reactants. The similar electronic structure element in the NBO approach is a lone vacancy on the carbonyl carbon atom in the reactive species. The electronic structure patterns revealed in the NBO and QTAIM-based analyses consistently clarify the reactivity issues in this system.     

Dynamic structures of phosphodiesterase-5 active site by combined molecular dynamics simulations and hybrid quantum mechanical/molecular mechanical calculations

Various quantum mechanical/molecular mechanical (QM/MM) geometry optimizations starting from an x-ray crystal structure and from the snapshot structures of constrained molecular dynamics (MD) simulations have been performed to characterize two dynamically stable active site structures of phosphodiesterase-5 (PDE5) in solution. The only difference between the two PDE5 structures exists in the catalytic, second bridging ligand (BL2) which is HO- or H2O. It has been shown that, whereas BL2 (i.e. HO-) in the PDE5(BL2 = HO-) structure can really bridge the two positively charged metal ions (Zn2+ and Mg2+), BL2 (i.e. H2O) in the PDE5(BL2 = H2O) structure can only coordinate Mg2+. It has been demonstrated that the results of the QM/MM geometry optimizations are remarkably affected by the solvent water molecules, the dynamics of the protein environment, and the electronic embedding charges of the MM region in the QM part of the QMM/MM calculation. The PDE5(BL2 = H2O) geometries optimized by using the QM/MM method in different ways show strong couplings between these important factors. It is interesting to note that the PDE5(BL2 = HO-) and PDE5(BL2 = H2O) geometries determined by the QM/MM calculations neglecting these three factors are all consistent with the corresponding geometries determined by the QM/MM calculations that account for all of these three factors. These results suggest the overall effects of these three important factors on the optimized geometries can roughly cancel out. However, the QM/MM calculations that only account for some of these factors could lead to considerably different geometries. These results might be useful also in guiding future QM/MM geometry optimizations on other enzymes.     

Configuration Flipping in Distal Pocket of Multidrug Transporter MexB Impacts the Efflux Inhibitory Mechanism

MexAB-OprM efflux pumps, found in Pseudomonas aeruginosa, play a major role in drug resistance by extruding out drugs and antibiotic molecules from cells. Inhibitors are used to cease the potency of the efflux pumps. In this study, in-silico models are used to investigate the nature of the binding pocket of the MexAB-OprM efflux pump. First, we have performed classical molecular dynamics (MD) simulations to shed light on different aspects of protein–inhibitor interaction in the binding pocket of the pump. Using classical MD simulations, quantum mechanics/molecular mechanics (QM/MM), and various types of analyses, it is found that D13-9001 has a higher binding affinity towards the binding pocket compared to D1 and D2; the results are in sync with the experimental dat. Two stable configurations of D13-9001 are discovered inside the distal pocket which could be one of the primary reasons for the greater efficacy of D13-9001. The free energy barrier upon changing one state to another is calculated by employing umbrella sampling method. Finally, F178 is mutated to have the complete picture as it contributes significantly to the binding energy irrespective of the three inhibitors. Our results may help to design a new generation of inhibitors for such an efflux pump.     

Hydrogen‐bonding interactions in the active site of a low molecular weight protein‐tyrosine phosphatase

Molecular dynamics simulation of the Michaelis complex, phospho‐enzyme intermediate, and the wild‐type and C12S mutant have been carried out to examine hydrogen‐bonding interactions in the active site of the bovine low molecular weight protein‐tyrosine phosphatase (BPTP). It was found that the S_γ atom of the nucleophilic residue Cys‐12 is ideally located at a position opposite from the phenylphosphate dianion for an inline nucleophilic substitution reaction. In addition, electrostatic and hydrogen‐bonding interactions from the backbone amide groups of the phosphate‐binding loop strongly stabilize the thiolate anion, making Cys‐12 ionized in the active site. In the phospho‐enzyme intermediate, three water molecules are found to form strong hydrogen bonds with the phosphate group. In addition, another water molecule can be identified to form bridging hydrogen bonds between the phosphate group and Asp‐129, which may act as the nucleophile in the subsequent phosphate hydrolysis reaction, with Asp‐129 serving as a general base. The structural difference at the active site between the wild‐type and C12S mutant has been examined. It was found that the alkoxide anion is significantly shifted toward one side of the phosphate binding loop, away from the optimal position enjoyed by the thiolate anion of the wild‐type enzyme in an S_N2 process. This, coupled with the high pK_a value of an alcoholic residue, makes the C12S mutant catalytically inactive. These molecular dynamics simulations provided details of hydrogen bonding interactions in the active site of BPTP, and a structural basis for further studies using combined quantum mechanical and molecular mechanical potential to model the entire dephosphorylation reaction by BPTP. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1192–1203, 2000     

Interfacing the GROMOS (bio)molecular simulation software to quantum‐chemical program packages

The newly implemented quantum‐chemical/molecular‐mechanical (QM/MM) functionality of the Groningen molecular simulation (GROMOS) software for (bio)molecular simulation is described. The implementation scheme is based on direct coupling of the GROMOS C++ software to executables of the quantum‐chemical program packages MNDO and TURBOMOLE, allowing for an independent further development of these packages. The new functions are validated for different test systems using program and model testing techniques. The effect of truncating the QM/MM electrostatic interactions at various QM/MM cutoff radii is discussed and the application of semiempirical versus density‐functional Hamiltonians for a solute molecule in aqueous solution is compared. © 2012 Wiley Periodicals, Inc.     

Combined QM(DFT)/MM molecular dynamics simulations of the deamination of cytosine by yeast cytosine deaminase (yCD)

Extensive combined quantum mechanical (B3LYP/6‐31G*) and molecular mechanical (QM/MM) molecular dynamics simulations have been performed to elucidate the hydrolytic deamination mechanism of cytosine to uracil catalyzed by the yeast cytosine deaminase (yCD). Though cytosine has no direct binding to the zinc center, it reacts with the water molecule coordinated to zinc, and the adjacent conserved Glu64 serves as a general acid/base to shuttle protons from water to cytosine. The overall reaction consists of several proton‐transfer processes and nucleophilic attacks. A tetrahedral intermediate adduct of cytosine and water binding to zinc is identified and similar to the crystal structure of yCD with the inhibitor 2‐pyrimidinone. The rate‐determining step with the barrier of 18.0 kcal/mol in the whole catalytic cycle occurs in the process of uracil departure where the proton transfer from water to Glu64 and nucleophilic attack of the resulting hydroxide anion to C2 of the uracil ring occurs synchronously. © 2016 Wiley Periodicals, Inc.     

Elucidating the Dual Mode of Action of Dipeptidyl Enoates in the Inhibition of Rhodesain Cysteine Proteases

A computational study of the two possible inhibition mechanisms of rhodesain cysteine protease by the dipeptidyl enoate Cbz-Phe-Leu-CH=CH−CO₂C₂H₅ has been carried out by means of molecular dynamics simulations with hybrid QM/MM potentials. The low free energy barriers confirm that the Cys25 residue can attack both C_β and C1 atoms of the inhibitor, confirming a dual mode of action in the inhibition of the rhodesain by enoates. According to the results, the inhibition process through the Cys25 attack on the C_β atom of the inhibitor is an exergonic and irreversible process, while the inhibition process when Cys25 attacks on the C1 atom of the inhibitor is and exergonic but reversible process. The interactions between the inhibitor and rhodesain suggest that P2 is the most important fragment to consider in the design of new efficient inhibitors of rhodesain. These results may be useful for the design of new inhibitors of rhodesain and other related cysteine proteases based on dipeptidyl enoates scaffolds.     

A new method to locate saddle points for reactions in solution by using the free-energy gradient method and the mean field approximation

A new method for calculating saddle points of reactions in solution is presented. The main characteristics of the method are: (1) the solute-solvent system is described by the averaged solvent electrostatic potential/molecular dynamics method (ASEP/MD). This is a quantum mechanics/molecular mechanics method (QM/MM) that makes use of the mean field approximation (MFA) and that permits one to simultaneously optimize the electronic structure and geometry of the solute molecule and the solvent structure around it. (2) The transition state is located by the joint use of the free-energy gradient method and the mean field approximation. An application to the study of the Menshutkin reaction between NH(3) and CH(3)Cl in aqueous solution is discussed. The accuracy and usefulness of the proposed method is checked through comparison with other methods.     

Implementation of an adaptive umbrella sampling method for the calculation of multidimensional potential of mean force of chemical reactions in solution

We describe the implementation of an adaptive umbrella sampling method, making use of the weighted histogram analysis method, for computing multidimensional potential of mean force for chemical reaction in solution. The approach is illustrated by investigating the effect of aqueous solution on the free energy surface for the proton transfer reaction of [H(3)N-H-NH(3)](+) using a combined quantum mechanical and molecular mechanical AM1/TIP3P potential.     

Analytic first and second derivatives of the energy in the fragment molecular orbital method combined with molecular mechanics

Analytic first and second derivatives of the energy are developed for the fragment molecular orbital method interfaced with molecular mechanics in the electrostatic embedding scheme at the level of Hartree-Fock and density functional theory. The importance of the orbital response terms is demonstrated. The role of electrostatic embedding upon molecular vibrations is analyzed, comparing force field and quantum mechanical treatments for an ionic liquid and a solvated protein. The method is applied for 100 protein conformations sampled in molecular dynamics (MD) to take into account the complexity of a flexible protein structure in solution, and a good agreement with experimental data is obtained: Frequencies from an experimental infrared (IR) spectrum are reproduced within 17 cm⁻¹ .     

A QM/MM simulation study of transamination reaction at the active site of aspartate aminotransferase: Free energy landscape and proton transfer pathways

Transaminase is a key enzyme for amino acid metabolism, which reversibly catalyzes the transamination reaction with the help of PLP (pyridoxal 5^' -phosphate) as its cofactor. Here we have investigated the mechanism and free energy landscape of the transamination reaction involving the aspartate transaminase (AspTase) enzyme and aspartate-PLP (Asp-PLP) complex using QM/MM simulation and metadynamics methods. The reaction is found to follow a stepwise mechanism where the active site residue Lys258 acts as a base to shuttle a proton from α -carbon (CA) to imine carbon (C4A) of the PLP-Asp Schiff base. In the first step, the Lys258 abstracts the CA proton of the substrate leading to the formation of a carbanionic intermediate which is followed by the reprotonation of the Asp-PLP Schiff base at C4A atom by Lys258. It is found that the free energy barrier for the proton abstraction by Lys258 and that for the reprotonation are 17.85 and 3.57 kcal/mol, respectively. The carbanionic intermediate is 7.14 kcal/mol higher in energy than the reactant. Hence, the first step acts as the rate limiting step. The present calculations also show that the Lys258 residue undergoes a conformational change after the first step of transamination reaction and becomes proximal to C4A atom of the Asp-PLP Schiff base to favor the second step. The active site residues Tyr70* and Gly38 anchor the Lys258 in proper position and orientation during the first step of the reaction and stabilize the positive charge over Lys258 generated at the intermediate step.     

Increasing the time step with mass scaling in Born‐Oppenheimer ab initio QM/MM molecular dynamics simulations

Born‐Oppenheimer ab initio QM/MM molecular dynamics simulation with umbrella sampling is a state‐of‐the‐art approach to calculate free energy profiles of chemical reactions in complex systems. To further improve its computational efficiency, a mass‐scaling method with the increased time step in MD simulations has been explored and tested. It is found that by increasing the hydrogen mass to 10 amu, a time step of 3 fs can be employed in ab initio QM/MM MD simulations. In all our three test cases, including two solution reactions and one enzyme reaction, the resulted reaction free energy profiles with 3 fs time step and mass scaling are found to be in excellent agreement with the corresponding simulation results using 1 fs time step and the normal mass. These results indicate that for Born‐Oppenheimer ab initio QM/MM molecular dynamics simulations with umbrella sampling, the mass‐scaling method can significantly reduce its computational cost while has little effect on the calculated free energy profiles. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

Preorganization and reorganization as related factors in enzyme catalysis: the chorismate mutase case

In this paper a deeper insight into the chorismate-to prephenate-rearrangement, catalyzed by Bacillus subtilis chorismate mutase, is provided by means of a combination of statistical quantum mechanics/molecular mechanics simulation methods and hybrid potential energy surface exploration techniques. The main aim of this work is to present an estimation of the preorganization and reorganization terms of the enzyme catalytic rate enhancement. To analyze the first of these, we have studied different conformational equilibria of chorismate in aqueous solution and in the enzyme active site. Our conclusion is that chorismate mutase preferentially binds the reactive conformer of the substrate--that presenting a structure similar to the transition state of the reaction to be catalyzed--with shorter distances between the carbon atoms to be bonded and more diaxial character. With respect to the reorganization effect, an energy decomposition analysis of the potential energies of the reactive reactant and of the reaction transition state in aqueous solution and in the enzyme shows that the enzyme structure is better adapted to the transition structure. This means not only a more negative electrostatic interaction energy with the transition state but also a low enzyme deformation contribution to the energy barrier. Our calculations reveal that the structure of the enzyme is responsible for stabilizing the transition state structure of the reaction, with concomitant selection of the reactive form of the reactants. This is, the same enzymatic pattern that stabilizes the transition structure also promotes those reactant structures closer to the transition structure (i.e., the reactive reactants). In fact, both reorganization and preorganization effects have to be considered as the two faces of the same coin, having a common origin in the effect of the enzyme structure on the energy surface of the substrate.     

Molecular dynamics simulations of the detoxification of paraoxon catalyzed by phosphotriesterase

Combined QM(PM3)/MM molecular dynamics simulations together with QM(DFT)/MM optimizations for key configurations have been performed to elucidate the enzymatic catalysis mechanism on the detoxification of paraoxon by phosphotriesterase (PTE). In the simulations, the PM3 parameters for the phosphorous atom were reoptimized. The equilibrated configuration of the enzyme/substrate complex showed that paraoxon can strongly bind to the more solvent‐exposed metal ion Zn_β, but the free energy profile along the binding path demonstrated that the binding is thermodynamically unfavorable. This explains why the crystal structures of PTE with substrate analogues often exhibit long distances between the phosphoral oxygen and Zn_β. The subsequent S_N2 reaction plays the key role in the whole process, but controversies exist over the identity of the nucleophilic species, which could be either a hydroxide ion terminally coordinated to Zn_α or the μ‐hydroxo bridge between the α‐ and β‐metals. Our simulations supported the latter and showed that the rate‐limiting step is the distortion of the bound paraoxon to approach the bridging hydroxide. After this preparation step, the bridging hydroxide ion attacks the phosphorous center and replaces the diethyl phosphate with a low barrier. Thus, a plausible way to engineer PTE with enhanced catalytic activity is to stabilize the deformed paraoxon. Conformational analyses indicate that Trp131 is the closest residue to the phosphoryl oxygen, and mutations to Arg or Gln or even Lys, which can shorten the hydrogen bond distance with the phosphoryl oxygen, could potentially lead to a mutant with enhanced activity for the detoxification of organophosphates. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2009     

锌酶的计算模拟:挑战与最新进展

锌酶在人体中分布非常广泛,种类繁多,是当前最受关注的金属酶之一。由于在锌配位结构上的多样性以及Zn²⁺饱和的d轨道带来的“光谱寂静”性,导致许多实验研究手段受限。计算模拟在锌酶的研究中发挥着越来越重要的作用,已经成为不可或缺的研究工具。现代量子化学计算模拟方法,特别是被视为研究生物大分子体系非常有效的QM/MM组合方法,目前已经被广泛应用于探讨复杂多变的锌配位结构以及锌酶催化反应机理。通过在QM/MM水平下开展的分子动力学模拟,可以揭示锌酶体系中结构与功能间的相互关系。此外,分子力场方法在锌酶研究中同样发挥了不可替代的作用,由于传统力场普遍无法正确描述锌配位结构,因此,锌酶分子力场的开发具有迫切的现实意义。本文总结了近年来锌酶计算模拟领域的最新进展,提出了锌酶计算研究中还有待解决的一些问题。     

Intra‐ and intermolecular interactions in crystals of polar molecules. A study by the mixed quantum mechanical/molecular mechanical SCMP‐NDDO method

Stabilization energies of crystals of polar molecules were calculated with the recently developed NDDO‐SCMP method that determines the wave function of a subunit embedded in the symmetrical environment constituted by the copies of the subunit. The total stabilization energies were decomposed into four components. The deformation energy is the difference between the energy of the molecule in the geometries adopted in the crystal on the one hand, and in vacuo, on the other hand. Further energy components are derived from the molecular geometry found in the crystal phase. The electrostatic component is the interaction energy of the molecule with the crystal field, corresponding to the charge distribution obtained in vacuo. The polarization component is the energy lowering resulted in the self‐consistent optimization of the wave function in the crystal field. The rest of the stabilization energy is attributed to the dispersion–repulsion component, and is calculated from an empirical potential function. The major novelty of this decomposition scheme is the introduction of the deformation energy. It requires the optimization of the structural parameters, including the molecular geometry, the intermolecular coordinates, and the cell parameters of the crystal. The optimization is performed using the recently implemented forces in the SCMP‐NDDO method, and this new feature is discussed in detail. The calculation of the deformation energy is particularly important to obtain stabilization energies for crystals in which the molecular geometry differs considerably from that corresponding to the energy minimum of the isolated molecule. As an example, crystals of diastereoisomeric salts are investigated. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 1679–1690, 2001     

CPMD/GULP QM/MM interface for modeling periodic solids: Implementation and its application in the study of Y‐zeolite supported Rhn clusters

We report here the development of hybrid quantum mechanics/molecular mechanics (QM/MM) interface between the plane‐wave density functional theory based CPMD code and the empirical force‐field based GULP code for modeling periodic solids and surfaces. The hybrid QM/MM interface is based on the electrostatic coupling between QM and MM regions. The interface is designed for carrying out full relaxation of all the QM and MM atoms during geometry optimizations and molecular dynamics simulations, including the boundary atoms. Both Born–Oppenheimer and Car–Parrinello molecular dynamics schemes are enabled for the QM part during the QM/MM calculations. This interface has the advantage of parallelization of both the programs such that the QM and MM force evaluations can be carried out in parallel to model large systems. The interface program is first validated for total energy conservation and parallel scaling performance is benchmarked. Oxygen vacancy in α‐cristobalite is then studied in detail and the results are compared with a fully QM calculation and experimental data. Subsequently, we use our implementation to investigate the structure of rhodium cluster (Rh_n; n = 2 to 6) formed from Rh(C₂H₄)₂ complex adsorbed within a cavity of Y‐zeolite in a reducible atmosphere of H₂ gas. © 2016 Wiley Periodicals, Inc.