Binding free energies for nicotine analogs inhibiting cytochrome P450 2A6 by a combined use of molecular dynamics simulations and QM/MM-PBSA calculations

Molecular dynamics (MD) simulations and hybrid quantum mechanical/molecular mechanical (QM/MM) calculations have been performed to explore the dynamic behaviors of cytochrome P450 2A6 (CYP2A6) binding with nicotine analogs (that are typical inhibitors) and to calculate their binding free energies in combination with Poisson–Boltzmann surface area (PBSA) calculations. The combined MD simulations and QM/MM-PBSA calculations reveal that the most important structural parameters affecting the CYP2A6-inhibitor binding affinity are two crucial internuclear distances, that is, the distance between the heme iron atom of CYP2A6 and the coordinating atom of the inhibitor, and the hydrogen-bonding distance between the N297 side chain of CYP2A6 and the pyridine nitrogen of the inhibitor. The combined MD simulations and QM/MM-PBSA calculations have led to dynamic CYP2A6-inhibitor binding structures that are consistent with the observed dynamic behaviors and structural features of CYP2A6-inhibitor binding, and led to the binding free energies that are in good agreement with the experimentally-derived binding free energies. The agreement between the calculated binding free energies and the experimentally-derived binding free energies suggests that the combined MD and QM/MM-PBSA approach may be used as a valuable tool to accurately predict the CYP2A6-inhibitor binding affinities in future computational design of new, potent and selective CYP2A6 inhibitors.     

Harder,better, faster,stronger: Large-scale QM and QM/MM for predictive modeling in enzymes and proteins

Computational prediction of enzyme mechanism and protein function requires accurate physics-based models and suitable sampling. We discuss recent advances in large-scale quantum mechanical (QM) modeling of biochemical systems that have reduced the cost of high-accuracy models. Tradeoffs between sampling and accuracy have motivated modeling with molecular mechanics (MM) in a multiscale QM/MM or iterative approach. Limitations to both conventional density-functional theory and classical MM force fields remain for describing noncovalent interactions in comparison to experiment or wavefunction theory. Because predictions of enzyme action (i.e. electrostatics), free energy barriers, and mechanisms are sensitive to the protocol and embedding method in QM/MM, convergence tests and systematic methods for quantifying QM-level interactions are a needed, active area of development.     

The reaction mechanism of paraoxon hydrolysis by phosphotriesterase from combined QM/MM simulations

Molecular dynamics simulations employing combined quantum mechanical and molecular mechanical (QM/MM) potentials have been carried out to investigate the reaction mechanism of the hydrolysis of paraoxon by phosphotriesterase (PTE). We used a dual-level QM/MM approach that synthesizes accurate results from high-level electronic structure calculations with computational efficiency of semiempirical QM/MM potentials for free energy simulations. In particular, the intrinsic (gas-phase) energies of the active site in the QM region are determined by using density functional theory (B3LYP) and second-order M?ller-Plesset perturbation theory (MP2) and the molecular dynamics free energy simulations are performed by using the mixed AM1:CHARMM potential. The simulation results suggest a revised mechanism for the phosphotriester hydrolysis mechanism by PTE. The reaction free energy profile is mirrored by structural motions of the binuclear metal center in the active site. The two zinc ions occupy a compact conformation with an average zinc-zinc distance of 3.5 +/- 0.1 A in the Michaelis complex, whereas it is elongated to 5.3 +/- 0.3 A at the transition state and product state. The substrate is loosely bound to the more exposed zinc ion (Znbeta2+) at an average distance of 3.8 A +/- 0.3 A. The P=O bond of the substrate paraoxon is activated by adopting a tight coordination to the Znbeta2+, releasing the coordinate to the bridging hydroxide ion and increasing its nucleophilicity. It was also found that a water molecule enters into the binding pocket of the loosely bound binuclear center, originally occupied by the nucleophilic hydroxide ion. We suggest that the proton of this water molecule is taken up by His254 at low pH or released to the solvent at high pH, resulting in a hydroxide ion that pulls the Znbeta2+ ion closer to form the compact configuration and restores the resting state of the enzyme.     

Combined quantum and molecular mechanics calculations on metalloproteins

The combination of quantum mechanics and molecular mechanics (QM/MM) methods is one of the most promising approaches to study the structure, function and properties of proteins. The number of QM/MM applications on metalloproteins is steadily increasing, especially studies with density functional methods on redox-active metal centres. Recent developments include new parameterised methods to treat covalent bonds between the quantum and classical systems, methods to obtain free energy from QM/MM results, and the combination of quantum chemistry and protein crystallography.     

Peptoid conformational free energy landscapes from implicit-solvent molecular simulations in AMBER

To test the accuracy of existing AMBER force field models in predicting peptoid conformation and dynamics, we simulated a set of model peptoid molecules recently examined by Butterfoss et al. (JACS 2009, 131, 16798-16807) using QM methods as well as three peptoid sequences with experimentally determined structures. We found that AMBER force fields, when used with a Generalized Born/Surface Area (GBSA) implicit solvation model, could accurately reproduce the peptoid torsional landscape as well as the major conformers of known peptoid structures. Enhanced sampling by replica exchange molecular dynamics (REMD) using temperatures from 300 to 800 K was used to sample over cis-trans isomerization barriers. Compared to (Nrch)5 and cyclo-octasarcosyl, the free energy of N-(2-nitro-3-hydroxyl phenyl)glycine-N-(phenyl)glycine has the most "foldable" free energy landscape, due to deep trans-amide minima dictated by N-aryl sidechains. For peptoids with (S)-N (1-phenylethyl) (Nspe) side chains, we observe a discrepancy in backbone dihedral propensities between molecular simulations and QM calculations, which may be due to force field effects or the inability to capture n --> n* interactions. For these residues, an empirical phi-angle biasing potential can "rescue" the backbone propensities seen in QM. This approach can serve as a general strategy for addressing force fields without resorting to a complete reparameterization. Overall, this study demonstrates the utility of implicit-solvent REMD simulations for efficient sampling to predict peptoid conformational landscapes, providing a potential tool for first-principles design of sequences with specific folding properties.     

Determinants of reactivity and selectivity in soluble epoxide hydrolase from quantum mechanics/molecular mechanics modeling

Soluble epoxide hydrolase (sEH) is an enzyme involved in drug metabolism that catalyzes the hydrolysis of epoxides to form their corresponding diols. sEH has a broad substrate range and shows high regio- and enantioselectivity for nucleophilic ring opening by Asp333. Epoxide hydrolases therefore have potential synthetic applications. We have used combined quantum mechanics/molecular mechanics (QM/MM) umbrella sampling molecular dynamics (MD) simulations (at the AM1/CHARMM22 level) and high-level ab initio (SCS-MP2) QM/MM calculations to analyze the reactions, and determinants of selectivity, for two substrates: trans-stilbene oxide (t-SO) and trans-diphenylpropene oxide (t-DPPO). The calculated free energy barriers from the QM/MM (AM1/CHARMM22) umbrella sampling MD simulations show a lower barrier for phenyl attack in t-DPPO, compared with that for benzylic attack, in agreement with experiment. Activation barriers in agreement with experimental rate constants are obtained only with the highest level of QM theory (SCS-MP2) used. Our results show that the selectivity of the ring-opening reaction is influenced by several factors, including proximity to the nucleophile, electronic stabilization of the transition state, and hydrogen bonding to two active site tyrosine residues. The protonation state of His523 during nucleophilic attack has also been investigated, and our results show that the protonated form is most consistent with experimental findings. The work presented here illustrates how determinants of selectivity can be identified from QM/MM simulations. These insights may also provide useful information for the design of novel catalysts for use in the synthesis of enantiopure compounds.     

Multiscale methods for macromolecular simulations

In this article we review the key modeling tools available for simulating biomolecular systems. We consider recent developments and representative applications of mixed quantum mechanics/molecular mechanics (QM/MM), elastic network models (ENMs), coarse-grained molecular dynamics, and grid-based tools for calculating interactions between essentially rigid protein assemblies. We consider how the different length scales can be coupled, both in a sequential fashion (e.g. a coarse-grained or grid model using parameterization from MD simulations), and via concurrent approaches, where the calculations are performed together and together control the progression of the simulation. We suggest how the concurrent coupling approach familiar in the context of QM/MM calculations can be generalized, and describe how this has been done in the CHARMM macromolecular simulation package.     

Modelling flavin and substrate substituent effects on the activation barrier and rate of oxygen transfer by p-hydroxybenzoate hydroxylase

The simulation of enzymatic reactions, using computer models, is becoming a powerful tool in the most fundamental challenge in biochemistry: to relate the catalytic activity of enzymes to their structure. In the present study, various computed parameters were correlated with the natural logarithm of experimental rate constants for the hydroxylation of various substrate derivatives catalysed by wild-type para-hydroxybenzoate hydroxylase (PHBH) as well as for the hydroxylation of the native substrate (p-hydroxybenzoate) by PHBH reconstituted with a series of 8-substituted flavins. The following relative parameters have been calculated and tested: (a) energy barriers from combined quantum mechanical/molecular mechanical (QM/MM) (AM1/CHARMM) reaction pathway calculations, (b) gas-phase reaction enthalpies (AM1) and (c) differences between the HOMO and LUMO energies of the isolated substrate and cofactor molecules (AM1 and B3LYP/6-31+G(d)). The gas-phase approaches yielded good correlations, as long as similarly charged species are involved. The QM/MM approach resulted in a good correlation, even including differently charged species. This indicates that the QM/MM model accounts quite well for the solvation effects of the active site surroundings, which vary for differently charged species. The correlations obtained demonstrate quantitative structure activity relationships for an enzyme-catalysed reaction including, for the first time, substitutions on both substrate and cofactor.     

Catalytic mechanism and energy barriers for butyrylcholinesterase-catalyzed hydrolysis of cocaine

The geometries of the transition states, intermediates, and prereactive enzyme-substrate complex and the corresponding energy barriers have been determined by performing hybrid quantum mechanical/molecular mechanical (QM/MM) calculations on butyrylcholinesterase (BChE)-catalyzed hydrolysis of (-)- and (+)-cocaine. The energy barriers were evaluated by performing QM/MM calculations with the QM method at the MP2/6-31+G* level and the MM method using the AMBER force field. These calculations allow us to account for the protein environmental effects on the transition states and energy barriers of these enzymatic reactions, showing remarkable effects of the protein environment on intermolecular hydrogen bonding (with an oxyanion hole), which is crucial for the transition state stabilization and, therefore, on the energy barriers. The calculated energy barriers are consistent with available experimental kinetic data. The highest barrier calculated for BChE-catalyzed hydrolysis of (-)- and (+)-cocaine is associated with the third reaction step, but the energy barrier calculated for the first step is close to the highest and is so sensitive to the protein environment that the first reaction step can be rate determining for (-)-cocaine hydrolysis catalyzed by a BChE mutant. The computational results provide valuable insights into future design of BChE mutants with a higher catalytic activity for (-)-cocaine.     

Comparison of end-point continuum-solvation methods for the calculation of protein-ligand binding free energies

We have compared the predictions of ligand‐binding affinities from several methods based on end‐point molecular dynamics simulations and continuum solvation, that is, methods related to MM/PBSA (molecular mechanics combined with Poisson–Boltzmann and surface area solvation). Two continuum‐solvation models were considered, viz., the Poisson–Boltzmann (PB) and generalised Born (GB) approaches. The nonelectrostatic energies were also obtained in two different ways, viz., either from the sum of the bonded, van der Waals, nonpolar solvation energies, and entropy terms (as in MM/PBSA), or from the scaled protein–ligand van der Waals interaction energy (as in the linear interaction energy approach, LIE). Three different approaches to calculate electrostatic energies were tested, viz., the sum of electrostatic interaction energies and polar solvation energies, obtained either from a single simulation of the complex or from three independent simulations of the complex, the free protein, and the free ligand, or the linear‐response approximation (LRA). Moreover, we investigated the effect of scaling the electrostatic interactions by an effective internal dielectric constant of the protein (?_int). All these methods were tested on the binding of seven biotin analogues to avidin and nine 3‐amidinobenzyl‐1H‐indole‐2‐carboxamide inhibitors to factor Xa. For avidin, the best results were obtained with a combination of the LIE nonelectrostatic energies with the MM+GB electrostatic energies from a single simulation, using ?_int = 4. For fXa, standard MM/GBSA, based on one simulation and using ?_int = 4–10 gave the best result. The optimum internal dielectric constant seems to be slightly higher with PB than with GB solvation. © Proteins 2012; © 2012 Wiley Periodicals, Inc.     

Molecular dynamics simulations of the intramolecular proton transfer and carbanion stabilization in the pyridoxal 5'-phosphate dependent enzymes L-dopa decarboxylase and alanine racemase

Molecular dynamics simulations using a combined quantum mechanical and molecular mechanical (QM/MM) potential have been carried out to investigate the internal proton transfer equilibrium of the external aldimine species in l-dopa decarboxylase, and carbanion stabilization by the enzyme cofactor in the active site of alanine racemase. Solvent effects lower the free energy of the O-protonated PLP tautomer both in aqueous solution and in the active site, resulting a free energy difference of about -1 kcal/mol relative to the N-protonated Schiff base in the enzyme. The external aldimine provides the dominant contribution to lowering the free energy barrier for the spontaneous decarboxylation of l-dopa in water, by a remarkable 16 kcal/mol, while the enzyme l-dopa decarboxylase further lowers the barrier by 8 kcal/mol. Kinetic isotope effects were also determined using a path integral free energy perturbation theory on the primary (13)C and the secondary (2)H substitutions. In the case of alanine racemase, if the pyridine ring is unprotonated as that in the active site, there is destabilizing contribution to the formation of the α-carbanion in the gas phase, although when the pyridine ring is protonated the contribution is stabilizing. In aqueous solution and in alanine racemase, the α-carbanion is stabilized both when the pyridine ring is protonated and unprotonated. The computational studies illustrated in this article show that combined QM/MM simulations can help provide a deeper understanding of the mechanisms of PLP-dependent enzymes. This article is part of a Special Issue entitled: Pyridoxal Phosphate Enzymology.     

Characterization of a catalytic ligand bridging metal ions in phosphodiesterases 4 and 5 by molecular dynamics simulations and hybrid quantum mechanical/molecular mechanical calculations

Cyclic nucleotide phosphodiesterases (PDEs) constitute a large superfamily of enzymes regulating concentrations of intracellular second messengers cAMP and cGMP through PDE-catalyzed hydrolysis. Although three-dimensional x-ray crystal structures of PDE4 and PDE5 have been reported, it is uncertain whether a critical, second bridging ligand (BL2) in the active site is H2O or HO- because hydrogen atoms cannot be determined by x-ray diffraction. The identity of BL2 is theoretically determined by performing molecular dynamics simulations and hybrid quantum mechanical/molecular mechanical (QM/MM) calculations, for the first time, on the protein structures resolved by x-ray diffraction. The computational results confirm our previous suggestion, which was based on QM calculations on a simplified active site model, that BL2 in PDE4 should be HO-, rather than H2O, serving as the nucleophile to initialize the catalytic hydrolysis of cAMP. The molecular dynamics simulations and QM/MM calculations on PDE5 demonstrate for the first time that the BL2 in PDE5 should also be HO- rather than H2O as proposed in recently published reports on the x-ray crystal structures, which serves as the nucleophile to initialize the PDE5-catalyzed hydrolysis of cGMP. These fundamental structural insights provide a rational basis for future structure-based drug design targeting PDEs.     

Molecular determinants of xenobiotic metabolism: QM/MM simulation of the conversion of 1-chloro-2,4-dinitrobenzene catalyzed by M1-1 glutathione S-transferase

Modeling methods allow the identification and analysis of determinants of reactivity and specificity in enzymes. The reaction between glutathione and 1-chloro-2,4-dinitrobenzene (CDNB) is widely used as a standard activity assay for glutathione S-transferases (GSTs). It is important to understand the causes of differences between catalytic GST isoenzymes and the effects of mutations and genetic polymorphisms. Quantum mechanical/molecular mechanical (QM/MM) molecular dynamics simulations have been performed here to investigate the addition of the glutathione anion to CDNB in the wild-type M1-1 GST isoenzyme from rat and in three single point mutant (Tyr6Phe, Tyr115Phe, and Met108Ala) M1-1 GST enzymes. We have developed a specifically parameterized QM/MM method (AM1-SRP/CHARMM22) to model this reaction by fitting to experimental heats of formation and ionization potentials. Free energy profiles were obtained from molecular dynamics simulations of the reaction using umbrella sampling and weighted histogram analysis techniques. The reaction in solution has also been simulated and is compared to the enzymatic reaction. The free energies are in excellent agreement with experimental results. Overall the results of the present study show that QM/MM reaction pathway analysis provides detailed insight into the chemistry of GST and can be used to obtain mechanistic insight into the effects of specific mutations on this catalytic process.     

Protonation states of intermediates in the reaction mechanism of [NiFe] hydrogenase studied by computational methods

The [NiFe] hydrogenases catalyse the reversible conversion of H₂ to protons and electrons. The active site consists of a Fe ion with one carbon monoxide, two cyanide, and two cysteine (Cys) ligands. The latter two bridge to a Ni ion, which has two additional terminal Cys ligands. It has been suggested that one of the Cys residues is protonated during the reaction mechanism. We have used combined quantum mechanical and molecular mechanics (QM/MM) geometry optimisations, large QM calculations with 817 atoms, and QM/MM free energy simulations, using the TPSS and B3LYP methods with basis sets extrapolated to the quadruple zeta level to determine which of the four Cys residues is more favourable to protonate for four putative states in the reaction mechanism, Ni-SI_a, Ni-R, Ni-C, and Ni-L. The calculations show that for all states, the terminal Cys-546 residue is most easily protonated by 14–51 kJ/mol, owing to a more favourable hydrogen-bond pattern around this residue in the protein.     

Proton transfer in carbonic anhydrase is controlled by electrostatics rather than the orientation of the acceptor

Combined quantum mechanical/molecular mechanical (QM/MM) simulations are carried out to analyze factors that dictate the proton transfer in carbonic anhydrase II (CAII), an enzyme that has been used as a prototypical example of long-range proton transfers in biomolecules. In contrast to the long-held conjecture in the experimental literature, the computed potentials of mean force (PMF) suggest that the proton transfer in CAII is not very sensitive to the orientation of the acceptor group (His 64) and, therefore, the number of water molecules that bridge the donor (zinc-water) and acceptor groups. Perturbative analysis indicates that a series of polar and charged residues close to the transfer pathways make the dominant contribution to the barrier and exothermicity of the proton transfer reaction, thus supporting the proposal from previous studies of Warshel and co-workers using a somewhat simpler QM/MM model that electrostatic interactions play a major role in the proton transfer in CAII. The PMF results are in striking contrast to previous analysis using the same QM/MM method but an ensemble of minimum energy path (MEP) calculations, which found a steep dependence of the barrier height on the number of bridging water molecules. Analysis of the configurations sampled in the PMF and MEP simulations suggests that this difference arises because the PMF simulations sample a largely stepwise mechanism while the local MEP calculations artificially favored concerted transfers due to the specific protocol used to generate the initial configurations. Therefore, this study presents a compelling argument for carrying out proper conformational sampling in the study of long-range proton transfers. Finally, we illustrate that Phi analysis, which has been widely used in protein folding studies, can potentially generate new mechanistic information for long-range proton transfers regarding the sequence of events. The results of the perturbation analysis and the Phi analysis provide opportunities for experimentally testing the mechanistic proposals from this study and our recent work in which a stepwise "proton hole" transfer pathway has been proposed.     

Comparison of a QM/MM force field and molecular mechanics force fields in simulations of alanine and glycine "dipeptides" (Ace-Ala-Nme and Ace-Gly-Nme) in water in relation to the problem of modeling the unfolded peptide backbone in solution

We compare the conformational distributions of Ace-Ala-Nme and Ace-Gly-Nme sampled in long simulations with several molecular mechanics (MM) force fields and with a fast combined quantum mechanics/molecular mechanics (QM/MM) force field, in which the solute's intramolecular energy and forces are calculated with the self-consistent charge density functional tight binding method (SCCDFTB), and the solvent is represented by either one of the well-known SPC and TIP3P models. All MM force fields give two main states for Ace-Ala-Nme, beta and alpha separated by free energy barriers, but the ratio in which these are sampled varies by a factor of 30, from a high in favor of beta of 6 to a low of 1/5. The frequency of transitions between states is particularly low with the amber and charmm force fields, for which the distributions are noticeably narrower, and the energy barriers between states higher. The lower of the two barriers lies between alpha and beta at values of psi near 0 for all MM simulations except for charmm22. The results of the QM/MM simulations vary less with the choice of MM force field; the ratio beta/alpha varies between 1.5 and 2.2, the easy pass lies at psi near 0, and transitions between states are more frequent than for amber and charmm, but less frequent than for cedar. For Ace-Gly-Nme, all force fields locate a diffuse stable region around phi = pi and psi = pi, whereas the amber force field gives two additional densely sampled states near phi = +/-100 degrees and psi = 0, which are also found with the QM/MM force field. For both solutes, the distribution from the QM/MM simulation shows greater similarity with the distribution in high-resolution protein structures than is the case for any of the MM simulations.     

Theoretical approaches for dynamical ordering of biomolecular systems

Background

Living systems are characterized by the dynamic assembly and disassembly of biomolecules. The dynamical ordering mechanism of these biomolecules has been investigated both experimentally and theoretically. The main theoretical approaches include quantum mechanical (QM) calculation, all-atom (AA) modeling, and coarse-grained (CG) modeling. The selected approach depends on the size of the target system (which differs among electrons, atoms, molecules, and molecular assemblies). These hierarchal approaches can be combined with molecular dynamics (MD) simulation and/or integral equation theories for liquids, which cover all size hierarchies.

Refined models of New Delhi metallo-beta-lactamase-1 with inhibitors: an QM/MM modeling study

New Delhi metallo-beta-lactamase 1 (NDM-1) has been identified as a potential target for the treatment of multi-drug resistance bacterial infections. We used molecular docking, normal MD, SIE, QM/MM MD simulations, QM/MM GBSA binding free energy, and QM/MM GBSA alanine-scanning mutagenesis techniques to investigate interactions of the NDM-1 with 11 inhibitors (Tigecycline, BAL30072, D-captopril, Penicillin G, Ampicillin, Carbenicillin, Cephalexin, Cefaclor, Nitrocefin, Meropenem, and Imipenem). From our normal MD and QM/MM simulations, the correlation coefficients between the predicted binding free energies and experimental values are .88 and .93, respectively. Then simulations, which combined QM/MM/GBSA and alanine-scanning mutagenesis techniques, were performed and our results show that two residues (Lys211 and His250) have the strongest impact on the binding affinities of the 11 NDM-1/inhibitors. Therefore, our approach theoretically suggests that the two residues (Lys211 and His250) are responsible for the selectivity of NDM-1 associated inhibitors.