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.     

Protein environment facilitates O2 binding in non-heme iron enzyme. An insight from ONIOM calculations on isopenicillin N synthase (IPNS)

Binding of dioxygen to a non-heme enzyme has been modeled using the ONIOM combined quantum mechanical/molecular mechanical (QM/MM) method. For the present system, isopenicillin N synthase (IPNS), binding of dioxygen is stabilized by 8-10 kcal/mol for a QM:MM (B3LYP:Amber) protein model compared to a quantum mechanical model of the active site only. In the protein system, the free energy change of O2 binding is close to zero. Two major factors consistently stabilize O2 binding. The first effect, evaluated at the QM level, originates from a change in coordination geometry of the iron center. The active-site model artificially favors the deoxy state (O2 not bound) because it allows too-large rearrangements of the five-coordinate iron site. This error is corrected when the protein is included. The corresponding effect on binding energies is 3-6 kcal/mol, depending on the coordination mode of O2 (side-on or end-on). The second major factor that stabilizes O2 binding is van der Waals interactions between dioxygen and the surrounding enzyme. These interactions, 3-4 kcal/mol at the MM level, are neglected in models that include only the active site. Polarization of the active site by surrounding amino acids does not have a significant effect on the binding energy in the present system.     

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.     

Is the protein surrounding the active site critical for hydrogen peroxide reduction by selenoprotein glutathione peroxidase? An ONIOM study

In this ONIOM(QM:MM) study, we evaluate the role of the protein surroundings in the mechanism of H2O2 reduction catalyzed by the glutathione peroxidase enzyme, using the whole monomer (3113 atoms in 196 amino acid residues) as a model. A new optimization scheme that allows the full optimization of transition states for large systems has been utilized. It was found that in the presence of the surrounding protein the optimized active site structure bears a closer resemblance to the one in the X-ray structure than that without the surrounding protein. H2O2 reduction occurs through a two-step mechanism. In the first step, the selenolate anion (E-Se(-)) formation occurs with a barrier of 16.4 kcal/mol and is endothermic by 12.0 kcal/mol. The Gln83 residue plays the key role of the proton abstractor, which is in line with the experimental suggestion. In the second step, the O-O bond is cleaved, and selenenic acid (R-Se-OH) and a water molecule are formed. The calculated barrier for this process is 6.0 kcal/mol, and it is exothermic by 80.9 kcal/mol. The overall barrier of 18.0 kcal/mol for H2O2 reduction is in reasonable agreement with the experimentally measured barrier of 14.9 kcal/mol. The protein surroundings has been calculated to exert a net effect of only 0.70 kcal/mol (in comparison to the "active site only" model including solvent effects) on the overall barrier, which is most likely due to the active site being located at the enzyme surface.     

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.     

On the origin of the stabilization of the zwitterionic resting state of cysteine proteases: a theoretical study

Papain-like cysteine proteases are ubiquitous proteolytic enzymes. The protonated His199/deprotonated Cys29 ion pair (cathepsin B numbering) in the active site is essential for their proper functioning. The presence of this ion pair stands in contrast to the corresponding intrinsic residue p K a values, indicating a strong influence of the enzyme environment. In the present work we show by molecular dynamics simulations on quantum mechanical/molecular mechanical (QM/MM) potentials that the ion pair is stabilized by a complex hydrogen bond network which comprises several amino acids situated in the active site of the enzyme and 2-4 water molecules. QM/MM reaction path computations for the proton transfer from His199 to the thiolate of the Cys29 moiety indicate that the ion pair is about 32-36 kJ mol (-1) more stable than the neutral form if the whole hydrogen bonding network is active. Without any hydrogen bonding network the ion pair is predicted to be significantly less stable than the neutral form. QM/MM charge deletion analysis and QM model calculations are used to quantify the stabilizing effect of the active-site residues and the L1 helix in favor of the zwitterionic form. The active-site water molecules contribute about 30 kJ mol (-1) to the overall stabilization. Disruption of the hydrogen bonding network upon substrate binding is expected to enhance the nucleophilic reactivity of the thiolate.     

Geometry optimization with QM/MM,ONIOM, and other combined methods. I. Microiterations and constraints

Hybrid energy methods such as QM/MM and ONIOM, that combine different levels of theory into one calculation, have been very successful in describing large systems. Geometry optimization methods can take advantage of the partitioning of these calculations into a region treated at a quantum mechanical (QM) level of theory and the larger, remaining region treated by an inexpensive method such as molecular mechanics (MM). A series of microiterations can be employed to fully optimize the MM region for each optimization step in the QM region. Cartesian coordinates are used for the MM region and are chosen so that the internal coordinates of the QM region remain constant during the microiterations. The coordinates of the MM region are augmented to permit rigid body translation and rotation of the QM region. This is essential if any atoms in the MM region are constrained, but it also improves the efficiency of unconstrained optimizations. Because of the microiterations, special care is needed for the optimization step in the QM region so that the system remains in the same local valley during the course of the optimization. The optimization methodology with microiterations, constraints, and step-size control are illustrated by calculations on bacteriorhodopsin and other systems.     

Multistructural microiteration technique for geometry optimization and reaction path calculation in large systems

We propose a multistructural microiteration (MSM) method for geometry optimization and reaction path calculation in large systems. MSM is a simple extension of the geometrical microiteration technique. In conventional microiteration, the structure of the non‐reaction‐center (surrounding) part is optimized by fixing atoms in the reaction‐center part before displacements of the reaction‐center atoms. In this method, the surrounding part is described as the weighted sum of multiple surrounding structures that are independently optimized. Then, geometric displacements of the reaction‐center atoms are performed in the mean field generated by the weighted sum of the surrounding parts. MSM was combined with the QM/MM‐ONIOM method and applied to chemical reactions in aqueous solution or enzyme. In all three cases, MSM gave lower reaction energy profiles than the QM/MM‐ONIOM‐microiteration method over the entire reaction paths with comparable computational costs. © 2017 Wiley Periodicals, Inc.     

A multicentered approach to integrated QM/QM calculations. Applications to multiply hydrogen bonded systems

A multicentered integrated QM/QM technique has been developed. By separating high-level calculations in distinct regions of molecules, the multicentered approach supplants a single large high-level calculation with several smaller calculations. Due to the steep polynomial scaling of traditional ab initio quantum chemical methods, this separation significantly enhances the computational efficiency of QM/QM methods. The straightforward implementation of this multicentered approach is illustrated with several large poly-alcohols that form hydrogen bonds with water. The largest alcohol-water complex contains 81 atoms. For properly selected model systems, this multicentered approach introduces essentially no error in the dissociation energies of these complexes relative to conventional QM/QM schemes. This multicentered technique should be easily extended to other, more general integrated methods (QM/MM, ONIOM, etc).     

ONIOM approach for non-adiabatic on-the-fly molecular dynamics demonstrated for the backbone controlled Dewar valence isomerization

Non-adiabatic on-the-fly molecular dynamics (NA-O-MD) simulations require the electronic wavefunction, energy gradients, and derivative coupling vectors in every timestep. Thus, they are commonly restricted to the excited state dynamics of molecules with up to ≈20 atoms. We discuss an approximation that combines the ONIOM(QM:QM) method with NA-O-MD simulations to allow calculations for larger molecules. As a proof of principle we present the excited state dynamics of a (6-4)-lesion containing dinucleotide (63 atoms), and especially the importance to include the confinement effects of the DNA backbone. The method is able to include electron correlation on a high level of theory and offers an attractive alternative to QM:MM approaches for moderate sized systems with unknown force fields.     

Inhibitor binding by metallo-beta-lactamase IMP-1 from Pseudomonas aeruginosa: quantum mechanical/molecular mechanical simulations

The dynamics of the IMP-1 enzyme complexed with three prototypical inhibitors are investigated using a quantum mechanical/molecular mechanical (QM/MM) method based on the self-consistent-charge density-functional tight-binding model. The binding patterns of the inhibitors observed in X-ray diffraction experiments are well reproduced in 600 ps molecular dynamics simulations at room temperature. These inhibitors anchor themselves in the enzyme active site by direct coordination with the two zinc ions, displacing the hydroxide nucleophile that bridges the two zinc ions. In addition, they also interact with several active-site residues and those in two mobile loops. The excellent agreement with experimental structural data validates the QM/MM treatment used in our simulations.     

Computational methods for the study of enzymic reaction mechanisms III: a perturbation plus QM/MM approach for calculating relative free energies of protonation

We describe a coupling parameter, that is, perturbation, approach to effectively create and annihilate atoms in the quantum mechanical Hamiltonian within the closed shell restricted Hartree-Fock formalism. This perturbed quantum mechanical atom (PQA) method is combined with molecular mechanics (MM) methods (PQA/MM) within a molecular dynamics simulation, to model the protein environment (MM region) effects that also make a contribution to the overall free energy change. Using the semiempirical PM3 method to model the QM region, the application of this PQA/MM method is illustrated by calculation of the relative protonation free energy of the conserved OD2 (Asp27) and the N5 (dihydrofolate) proton acceptor sites in the active site of Escherichia coli dihydrofolate reductase (DHFR) with the bound nicotinamide adenine dinucleotide phosphate (NADPH) cofactor. For a number of choices for the QM region, the relative protonation free energy was calculated as the sum of contributions from the QM region and the interaction between the QM and MM regions via the thermodynamic integration (TI) method. The results demonstrate the importance of including the whole substrate molecule in the QM region, and the overall protein (MM) environment in determining the relative stabilities of protonation sites in the enzyme active site. The PQA/MM free energies obtained by TI were also compared with those estimated by a less computationally demanding nonperturbative method based on the linear response approximation (LRA). For some choices of QM region, the total free energies calculated using the LRA method were in very close agreement with the PQA/MM values. However, the QM and QM/MM component free energies were found to differ significantly between the two methods.     

Ab initio and QM/MM study of electron addition on the disulfide bond in thioredoxin

Thioredoxin controls the intracellular redox potential through a disulfide/dithiol couple. Under conditions of oxidative stress, this protein functions via one-electron exchange, in which formation of the disulfide radical anion occurs. Combined quantum mechanical (QM) and molecular mechanical (MM) calculations using two- and three-level ONIOM schemes were performed on the thioredoxin (Trx) protein of Chlamydomonas reinhardtii in its oxidized-disulfide and one-electron-reduced forms. In both cases, the active site disulfide moiety was described at the MP2(fc)/6-31+G(d) level, and larger regions of varying sizes around the active site were described at the B3LYP/6-31+G(d) level. The remainder of the 112 residues and 33 water molecules of the crystal structure (PDB entry 1EP7) were described by the AMBER force field. Adiabatic electron affinities were calculated for the disulfide bond in all systems. Separate QM or QM/QM calculations were performed on the QM regions to establish the role of the remainder of the protein on the active site properties. The radical anion species becomes more stable as the number of amide groups in the vicinity increases. One-electron reduction potentials were calculated for the small molecule models, and approximated for the protein for which the values are similar to the experimental one (approximately 0 V). This high reduction potential is due to interaction with the charged end of Lys40, as indicated by mutation in silico to norleucine. The inclusion of the protonated Asp30 side chain and a water molecule in the QM region leads to an increase in the electron affinity. Proton transfer from the Asp30 side chain to the Cys39 sulfur in the radical anion species is strongly disfavored. The radical anion is more stable than the protonated form, which is consistent with experimental results.     

Catalytic Mechanism of Cytochrome P450 2D6 for 4-Hydroxylation of Aripiprazole： A QM/MM Study

Drug metabolism is an important issue in drug discovery. Understanding how a drug is metabolized in the body will provide helpful information for lead optimization. Cytochrome P450 2D6 （CYP2D6） is a key enzyme for drug metabolism and responsible for the metabolism of about one third marketed drugs. Aripiprazole is an atypical an- tipsychotic and metabolized by CYP2D6 to its hydroxylated form. In this study, a series of computational methods were performed to understand how CYP2D6 accomplishes the 4-hydroxylation of aripiprazole. Molecular docking and molecular dynamics simulations were first performed to prepare the initial conformations for QM/MM calcula- tions. The results revealed two possible conformations for the drug-CYP2D6 complex. The ONIOM method for QM/MM calculations was then carried out to show detailed reaction pathways for the CYP2D6-catalyzed aripipra- zole hydroxylation reaction, which demonstrated that the dominant reactive channel was electrophilic and involved an initial attack on the n-system of the dichlorophenyl group of aripiprazole to produce cation δ-complex. Further- more, the product complex for each conformation was thermodynamically stable, which is in good agreement with previous reports.     

Zinc-homocysteine binding in cobalamin-dependent methionine synthase and its role in the substrate activation: DFT, ONIOM, and QM/MM molecular dynamics studies

Cobalamin-dependent methionine synthase (MetH) is an important metalloenzyme responsible for the biosynthesis of methionine. It catalyzes methyl transfer from N(5)-methyl-tetrahydrofolate to homocysteine (Hcy) by using a zinc ion to activate the Hcy substrate. Density functional theory (B3LYP) calculations on the active-site model in gas phase and in a polarized continuum model were performed to study the Zn coordination changes from the substrate-unbound state to the substrate-bound state. The protein effect on the Zn(2+) coordination exchange was further investigated by ONIOM (B3LYP:AMBER)-ME and EE calculations. The Zn(2+)-coordination exchange is found to be highly unfavorable in the gas phase with a high barrier and endothermicity. In the water solution, the reaction becomes exothermic and the reaction barrier is drastically decreased to about 10.0 kcal/mol. A considerable protein effect on the coordination exchange was also found; the reaction is even more exothermic and occurs without barrier. The enzyme was suggested to constrain the zinc coordination sphere in the reactant state (Hcy-unbound state) more than that in the product state (Hcy-bound state), which promotes ligation of the Hcy substrate. Molecular dynamics simulations using molecular mechanics (MM) and PM3/MM potentials suggest a correlation between the flexibility of the Zn(2+)-binding site and regulation of the enzyme function. Directed in silico mutations of selected residues in the active site were also performed. Our studies support a dissociative mechanism starting with the Zn-O(Asn234) bond breaking followed by the Zn-S((Hcy)) bond formation; the proposed associative mechanism for the Zn(2+)-coordination exchange is not supported.     

Computer simulation of the interaction of Cu(I) with cys residues at the binding site of the yeast metallochaperone Cu(I)-Atx1

The copper binding site and electronic structure of the metallochaperone protein Atx1 were investigated using the combination of quantum mechanics methods and molecular mechanics methods in the ONIOM(QM:MM) scheme at the density functional theory (DFT) B3LYP/ 6-31G(d):AMBER level. The residues in the binding site, -Met13-Thr14-Cys15-Cu(I)-Cys18-Gly17-Ser16-, were modeled with QM and the rest of the residues with MM. Our results indicate that the structure for Cu(I)-Atx1 has the copper atom coordinated to two sulfur atoms from Cys15 (2.110 A) and Cys18 (2.141 A) with an angle S-Cu(I) -S of 166 degrees . The potential energy surface of the copper atom is used to estimate its binding energy and the force field for the copper ligands. The potential surface is shallow for the bending mode S-Cu-S, which explains the origin of the disorder observed in crystallographic and nuclear magnetic resonance studies. Using molecular dynamics for Cu(I)-Atx1 in a box of water molecules and in vacuum, with the force field derived in this work, we observed a correlated motion between the side chains of Thr14 and of Lys65 which enhances distortions in the S-Cu-S geometry. The results are compared with recent experiments and the previous models. The vibrational spectra for the copper ligands and for the residues in the binding site were computed. The localized modes for the copper ligands and the amide bands were assigned. The presence of the copper atom affects the amide bands' frequencies of the residues Cys15 and Cys18, giving resolved bands that can be used to sense changes in the binding site upon translocation of copper atom or interaction with target proteins. Furthermore, the EXAFS (extended X-ray absorption fine structure) spectrum of the proposed structure for Cu(I)-Atx1 was calculated and reproduced the experiments fairly well.     

Clarification of the role of protein in carbonmonoxy myoglobin by investigating electronic states

This article reports the proton tautomerization effects of distal histidine residues in carbonmonoxy myoglobin according to the density functional calculations of the whole protein. The electron eigenstates and electrostatic potential (ESP) distributed around heme and its pocket vary significantly depending on the protonation positions of the distal histidine residues. To investigate the range over which the electronic structures are affected by the proton tautomerization, the quantum mechanics/molecular mechanics (QM/MM) method is applied to probe the QM size to reproduce the atomic partial charges and ESP around the active center. Consequently, we show that these properties converged for the 300 pm QM/MM system in this study. During the analysis, we also find that amino residues such as Phe43, Val68, and Phe138 interact strongly with heme through orbital mixing, indicating that the protein is a medium not only interacting with the reaction center, but also buffering on electrons. © 2013 Wiley Periodicals, Inc.     

molUP: A VMD plugin to handle QM and ONIOM calculations using the gaussian software

The notable advances obtained by computational (bio)chemistry provided its widespread use in many areas of science, in particular, in the study of reaction mechanisms. These studies involve a huge number of complex calculations, which are often carried out using the Gaussian suite of programs. The preparation of input files and the analysis of the output files are not easy tasks and often involve laborious and complex steps. Taking this into account, we developed molUP: a VMD plugin that offers a complete set of tools that enhance the preparation of QM and ONIOM (QM/MM, QM/QM, and QM/QM/MM) calculations. The starting structures for these calculations can be imported from different chemical formats. A set of tools is available to help the user to examine or modify any geometry parameter. This includes the definition of layers in ONIOM calculations, choosing fixed atoms during geometry optimizations, the recalculation or adjustment of the atomic charges, performing SCANs or IRC calculations, etc. molUP also extracts the geometries from the output files as well as the energies of each of them. All of these tasks are performed in an interactive GUI that is extremely helpful for the user. MolUP was developed to be easy to handle by inexperienced users, but simultaneously to be a fast and flexible graphical interface to allow the advanced users to take full advantage of this plugin. The program is available, free of charges, for macOS, Linux, and Windows at the PortoBioComp page https://www.fc.up.pt/PortoBioComp/database/doku.php?id=molup . © 2018 Wiley Periodicals, Inc.