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

Accounting for the instantaneous disorder in the enzyme-substrate Michaelis complex to calculate the Gibbs free energy barrier of an enzyme reaction

Many enzyme reactions present instantaneous disorder. These dynamic fluctuations in the enzyme-substrate Michaelis complexes generate a wide range of energy barriers that cannot be experimentally observed, but that determine the measured kinetics of the reaction. These individual energy barriers can be calculated using QM/MM methods, but then the problem is how to deal with this dispersion of energy barriers to provide kinetic information. So far, the most usual procedure has implied the so-called exponential average of the energy barriers. In this paper, we discuss the foundations of this method, and we use the free energy perturbation theory to derive an alternative equation to get the Gibbs free energy barrier of the enzyme reaction. In addition, we propose a practical way to implement it. We have chosen four enzyme reactions as examples. In particular, we have studied the hydrolysis of a glycosidic bond catalyzed by the enzyme Thermus thermophilus β-glycosidase, and the mutant Y284P Ttb-gly, and the hydrogen abstraction reactions from C13 and C7 of arachidonic acid catalyzed by the enzyme rabbit 15-lipoxygenase-1.

Computer-aided understanding and engineering of enzymatic selectivity

Enzymes offering chemo-, regio-, and stereoselectivity enable the asymmetric synthesis of high-value chiral molecules. Unfortunately, the drawback that naturally occurring enzymes are often inefficient or have undesired selectivity toward non-native substrates hinders the broadening of biocatalytic applications. To match the demands of specific selectivity in asymmetric synthesis, biochemists have implemented various computer-aided strategies in understanding and engineering enzymatic selectivity, diversifying the available repository of artificial enzymes. Here, given that the entire asymmetric catalytic cycle, involving precise interactions within the active pocket and substrate transport in the enzyme channel, could affect the enzymatic efficiency and selectivity, we presented a comprehensive overview of the computer-aided workflow for enzymatic selectivity. This review includes a mechanistic understanding of enzymatic selectivity based on quantum mechanical calculations, rational design of enzymatic selectivity guided by enzyme-substrate interactions, and enzymatic selectivity regulation via enzyme channel engineering. Finally, we discussed the computational paradigm for designing enzyme selectivity in silico to facilitate the advancement of asymmetric biosynthesis.

Mechanisms of metal-dependent non-redox decarboxylases from quantum chemical calculations

Quantum chemical calculations are today an extremely valuable tool for studying enzymatic reaction mechanisms. In this mini-review, we summarize our recent work on several metal-dependent decarboxylases, where we used the so-called cluster approach to decipher the details of the reaction mechanisms, including elucidation of the identity of the metal cofactors and the origins of substrate specificity.

Decarboxylases are of growing potential for biocatalytic applications, as they can be used in the synthesis of novel compounds of, e.g., pharmaceutical interest. They can also be employed in the reverse direction, providing a strategy to synthesize value‐added chemicals by CO₂ fixation. A number of non-redox metal-dependent decarboxylases from the amidohydrolase superfamily have been demonstrated to have promiscuous carboxylation activities and have attracted great attention in the recent years. The computational mechanistic studies provide insights that are important for the further modification and utilization of these enzymes in industrial processes. The discussed enzymes are: 5‐carboxyvanillate decarboxylase, γ‐resorcylate decarboxylase, 2,3‐dihydroxybenzoic acid decarboxylase, and iso-orotate decarboxylase.

Role of Structural Dynamics in Selectivity and Mechanism of Non-heme Fe(II) and 2-Oxoglutarate-Dependent Oxygenases Involved in DNA Repair

AlkB and its human homologue AlkBH2 are Fe(II)- and 2-oxoglutarate (2OG)-dependent oxygenases that repair alkylated DNA bases occurring as a consequence of reactions with mutagenic agents. We used molecular dynamics (MD) and combined quantum mechanics/molecular mechanics (QM/MM) methods to investigate how structural dynamics influences the selectivity and mechanisms of the AlkB- and AlkBH2-catalyzed demethylation of 3-methylcytosine (m3C) in single (ssDNA) and double (dsDNA) stranded DNA. Dynamics studies reveal the importance of the flexibility in both the protein and DNA components in determining the preferences of AlkB for ssDNA and of AlkBH2 for dsDNA. Correlated motions, including of a hydrophobic β-hairpin, are involved in substrate binding in AlkBH2-dsDNA. The calculations reveal that 2OG rearrangement prior to binding of dioxygen to the active site Fe is preferred over a ferryl rearrangement to form a catalytically productive Fe(IV)=O intermediate. Hydrogen atom transfer proceeds via a σ-channel in AlkBH2-dsDNA and AlkB-dsDNA; in AlkB-ssDNA, there is a competition between σ- and π-channels, implying that the nature of the complexed DNA has potential to alter molecular orbital interactions during the substrate oxidation. Our results reveal the importance of the overall protein-DNA complex in determining selectivity and how the nature of the substrate impacts the mechanism.

Using Atomic Confining Potentials for Geometry Optimization and Vibrational Frequency Calculations in Quantum-Chemical Models of Enzyme Active Sites

Quantum-chemical studies of enzymatic reaction mechanisms sometimes use truncated active-site models as simplified alternatives to mixed quantum mechanics molecular mechanics (QM/MM) procedures. Eliminating the MM degrees of freedom reduces the complexity of the sampling problem, but the trade-off is the need to introduce geometric constraints in order to prevent structural collapse of the model system during geometry optimizations that do not contain a full protein backbone. These constraints may impair the efficiency of the optimization, and care must be taken to avoid artifacts such as imaginary vibrational frequencies. We introduce a simple alternative in which terminal atoms of the model system are placed in soft harmonic confining potentials rather than being rigidly constrained. This modification is simple to implement and straightforward to use in vibrational frequency calculations, unlike iterative constraint-satisfaction algorithms, and allows the optimization to proceed without constraint even though the practical result is to fix the anchor atoms in space. The new approach is more efficient for optimizing minima and transition states, as compared to the use of fixed-atom constraints, and also more robust against unwanted imaginary frequencies. We illustrate the method by application to several enzymatic reaction pathways where entropy makes a significant contribution to the relevant reaction barriers. The use of confining potentials correctly describes reaction paths and facilitates calculation of both vibrational zero-point and finite-temperature entropic corrections to barrier heights.

Urea Derivatives in Modern Drug Discovery and Medicinal Chemistry

The urea functionality is inherent to numerous bioactive compounds, including a variety of clinically approved therapies. Urea containing compounds are increasingly used in medicinal chemistry and drug design in order to establish key drug-target interactions and fine-tune crucial drug-like properties. In this perspective, we highlight physicochemical and conformational properties of urea derivatives. We provide outlines of traditional reagents and chemical procedures for the preparation of ureas. Also, we discuss newly developed methodologies mainly aimed at overcoming safety issues associated with traditional synthesis. Finally, we provide a broad overview of urea-based medicinally relevant compounds, ranging from approved drugs to recent medicinal chemistry developments.

Conformational diversity induces nanosecond-timescale chemical disorder in the HIV-1 protease reaction pathway

The role of conformational diversity in enzyme catalysis has been a matter of analysis in recent studies. Pre-organization of the active site has been pointed out as the major source for enzymes' catalytic power. Following this line of thought, it is becoming clear that specific, instantaneous, non-rare enzyme conformations that make the active site perfectly pre-organized for the reaction lead to the lowest activation barriers that mostly contribute to the macroscopically observed reaction rate. The present work is focused on exploring the relationship between structure and catalysis in HIV-1 protease (PR) with an adiabatic mapping method, starting from different initial structures, collected from a classical MD simulation. The first, rate-limiting step of the HIV-1 PR catalytic mechanism was studied with the ONIOM QM/MM methodology (B3LYP/6-31G(d):ff99SB), with activation and reaction energies calculated at the M06-2X/6-311++G(2d,2p):ff99SB level of theory, in 19 different enzyme:substrate conformations. The results showed that the instantaneous enzyme conformations have two independent consequences on the enzyme's chemistry: they influence the barrier height, something also observed in the past in other enzymes, and they also influence the specific reaction pathway, which is something unusual and unexpected, challenging the "one enzyme-one substrate-one reaction mechanism" paradigm. Two different reaction mechanisms, with similar reactant probabilities and barrier heights, lead to the same gem-diol intermediate. Subtle nanosecond-timescale rearrangements in the active site hydrogen bonding network were shown to determine which reaction the enzyme follows. We named this phenomenon chemical disorder. The results make us realize the unexpected mechanistic consequences of conformational diversity in enzymatic reactivity.

Exploring Solanum tuberosum Epoxide Hydrolase Internal Architecture by Water Molecules Tracking

Several different approaches are used to describe the role of protein compartments and residues in catalysis and to identify key residues suitable for the modification of the activity or selectivity of the desired enzyme. In our research, we applied a combination of molecular dynamics simulations and a water tracking approach to describe the water accessible volume of Solanum tuberosum epoxide hydrolase. Using water as a molecular probe, we were able to identify small cavities linked with the active site: (i) one made up of conserved amino acids and indispensable for the proper positioning of catalytic water and (ii) two others in which modification can potentially contribute to enzyme selectivity and activity. Additionally, we identified regions suitable for de novo tunnel design that could also modify the catalytic properties of the enzyme. The identified hot-spots extend the list of the previously targeted residues used for modification of the regioselectivity of the enzyme. Finally, we have provided an example of a simple and elegant process for the detailed description of the network of cavities and tunnels, which can be used in the planning of enzyme modifications and can be easily adapted to the study of any other protein.

A Theoretical Study of the Benzoylformate Decarboxylase Reaction Mechanism

Density functional theory calculations are used to investigate the detailed reaction mechanism of benzoylformate decarboxylase, a thiamin diphosphate (ThDP)-dependent enzyme that catalyzes the nonoxidative decarboxylation of benzoylformate yielding benzaldehyde and carbon dioxide. A large model of the active site is constructed on the basis of the X-ray structure, and it is used to characterize the involved intermediates and transition states and evaluate their energies. There is generally good agreement between the calculations and available experimental data. The roles of the various active site residues are discussed and the results are compared to mutagenesis experiments. Importantly, the calculations identify off-cycle intermediate species of the ThDP cofactor that can have implications on the kinetics of the reaction.

Promoting Vibrations and the Function of Enzymes. Emerging Theoretical and Experimental Convergence

A complete understanding of enzyme catalysis requires knowledge of both transition state features and the detailed motions of atoms that cause reactant molecules to form and traverse the transition state. The seeming intractability of the problem arises from the femtosecond lifetime of chemical transition states, preventing most experimental access. Computational chemistry is admirably suited to short time scale analysis but can be misled by inappropriate starting points or by biased assumptions. Kinetic isotope effects provide an experimental approach to transition state structure and a method for obtaining transition state analogues but, alone, do not inform how that transition state is reached. Enzyme structures with transition state analogues provide computational starting points near the transition state geometry. These well-conditioned starting points, combined with the unbiased computational method of transition path sampling, provide realistic atomistic motions involved in transition state formation and passage. In many, but not all, enzymatic systems, femtosecond local protein motions near the catalytic site are linked to transition state formation. These motions are not inherently revealed by most approaches of transition state theory, because transition state theory replaces dynamics with the statistics of the transition state. Experimental and theoretical convergence of the link between local catalytic site vibrational modes and catalysis comes from heavy atom ("Born-Oppenheimer") enzymes. Fully labeled and catalytic site local heavy atom labels perturb the probability of finding enzymatic transition states in ways that can be analyzed and predicted by transition path sampling. Recent applications of these experimental and computational approaches reveal how subpicosecond local catalytic site protein modes play important roles in creating the transition state.

Combined Quantum Mechanics and Molecular Mechanics Studies of Enzymatic Reaction Mechanisms

The combined quantum mechanics/molecular mechanics (QM/MM) methods have become a valuable tool in computational biochemistry and received versatile applications for studying the reaction mechanisms of enzymes. The approach combines the calculations of the electronic structure of the active site by QM, with modeling of the protein environment using MM force field, which allows the long-range electrostatics and steric effects on the enzyme reactivity to be accounted for. In this review, we review some key theoretical and computational aspects of the method and we also present some applications to particular enzymatic reactions such as tryptophan-7-halogenase, cyclooxygenase-1, and the epidermal growth factor receptor.

Recent Trends in Quantum Chemical Modeling of Enzymatic Reactions

The quantum chemical cluster approach is a powerful method for investigating enzymatic reactions. Over the past two decades, a large number of highly diverse systems have been studied and a great wealth of mechanistic insight has been developed using this technique. This Perspective reviews the current status of the methodology. The latest technical developments are highlighted, and challenges are discussed. Some recent applications are presented to illustrate the capabilities and progress of this approach, and likely future directions are outlined.

Probing the orientation of inhibitor and epoxy-eicosatrienoic acid binding in the active site of soluble epoxide hydrolase

Soluble epoxide hydrolase (sEH) is an important therapeutic target of many diseases, such as chronic obstructive pulmonary disease (COPD) and diabetic neuropathic pain. It acts by hydrolyzing and thus regulating specific bioactive long chain polyunsaturated fatty acid epoxides (lcPUFA), like epoxyeicosatrienoic acids (EETs). To better predict which epoxides could be hydrolyzed by sEH, one needs to dissect the important factors and structural requirements that govern the binding of the substrates to sEH. This knowledge allows further exploration of the physiological role played by sEH. Unfortunately, a crystal structure of sEH with a substrate bound has not yet been reported. In this report, new photoaffinity mimics of a sEH inhibitor and EET regioisomers were prepared and used in combination with peptide sequencing and computational modeling, to identify the binding orientation of different regioisomers and enantiomers of EETs into the catalytic cavity of sEH. Results indicate that the stereochemistry of the epoxide plays a crucial role in dictating the binding orientation of the substrate.

Methods for Efficiently and Accurately Computing Quantum Mechanical Free Energies for Enzyme Catalysis

Enzyme activity is inherently linked to free energies of transition states, ligand binding, protonation/deprotonation, etc.; these free energies, and thus enzyme function, can be affected by residue mutations, allosterically induced conformational changes, and much more. Therefore, being able to predict free energies associated with enzymatic processes is critical to understanding and predicting their function. Free energy simulation (FES) has historically been a computational challenge as it requires both the accurate description of inter- and intramolecular interactions and adequate sampling of all relevant conformational degrees of freedom. The hybrid quantum mechanical molecular mechanical (QM/MM) framework is the current tool of choice when accurate computations of macromolecular systems are essential. Unfortunately, robust and efficient approaches that employ the high levels of computational theory needed to accurately describe many reactive processes (ie, ab initio, DFT), while also including explicit solvation effects and accounting for extensive conformational sampling are essentially nonexistent. In this chapter, we will give a brief overview of two recently developed methods that mitigate several major challenges associated with QM/MM FES: the QM non-Boltzmann Bennett's acceptance ratio method and the QM nonequilibrium work method. We will also describe usage of these methods to calculate free energies associated with (1) relative properties and (2) along reaction paths, using simple test cases with relevance to enzymes examples.

Conformational diversity and enantioconvergence in potato epoxide hydrolase 1

Potato epoxide hydrolase 1 (StEH1) is a biocatalytically important enzyme that exhibits rich enantio- and regioselectivity in the hydrolysis of chiral epoxide substrates. In particular, StEH1 has been demonstrated to enantioconvergently hydrolyze racemic mixes of styrene oxide (SO) to yield (R)-1-phenylethanediol. This work combines computational, crystallographic and biochemical analyses to understand both the origins of the enantioconvergent behavior of the wild-type enzyme, as well as shifts in activities and substrate binding preferences in an engineered StEH1 variant, R-C1B1, which contains four active site substitutions (W106L, L109Y, V141K and I155V). Our calculations are able to reproduce both the enantio- and regioselectivities of StEH1, and demonstrate a clear link between different substrate binding modes and the corresponding selectivity, with the preferred binding modes being shifted between the wild-type enzyme and the R-C1B1 variant. Additionally, we demonstrate that the observed changes in selectivity and the corresponding enantioconvergent behavior are due to a combination of steric and electrostatic effects that modulate both the accessibility of the different carbon atoms to the nucleophilic side chain of D105, as well as the interactions between the substrate and protein amino acid side chains and active site water molecules. Being able to computationally predict such subtle effects for different substrate enantiomers, as well as to understand their origin and how they are affected by mutations, is an important advance towards the computational design of improved biocatalysts for enantioselective synthesis.

Discovery of enantioselectivity of urea inhibitors of soluble epoxide hydrolase

Soluble epoxide hydrolase (sEH) hydrolyzes epoxyeicosatrienoic acids (EETs) in the metabolic pathway of arachidonic acid and has been considered as an important therapeutic target for chronic diseases such as hypertension, diabetes and inflammation. Although many urea derivatives are known as sEH inhibitors, the enantioselectivity of the inhibitors is not highlighted in spite of the stereoselective hydrolysis of EETs by sEH. In an effort to explore the importance of enantioselectivity in the urea scaffold, a series of enantiomers with the stereocenter adjacent to the urea nitrogen atom were prepared. The selectivity of enantiomers of 1-(α-alkyl-α-phenylmethyl)-3-(3-phenylpropyl)ureas showed wide range differences up to 125 fold with the low IC50 value up to 13 nM. The S-configuration with planar phenyl and small alkyl groups at α-position is crucial for the activity and selectivity. However, restriction of the free rotation of two α-groups with indan-1-yl or 1,2,3,4-tetrahydronaphthalen-1-yl moiety abolishes the selectivity between the enantiomers, despite the increase in activity up to 13 nM. The hydrophilic group like sulfonamido group at para position of 3-phenylpropyl motif of 1-(α-alkyl-α-phenylmethyl-3-(3-phenylpropyl)urea improves the activity as well as enantiomeric selectivity. All these ureas are proved to be specific inhibitor of sEH without inhibition against mEH.

Expanding the Catalytic Triad in Epoxide Hydrolases and Related Enzymes

Potato epoxide hydrolase 1 exhibits rich enantio- and regioselectivity in the hydrolysis of a broad range of substrates. The enzyme can be engineered to increase the yield of optically pure products as a result of changes in both enantio- and regioselectivity. It is thus highly attractive in biocatalysis, particularly for the generation of enantiopure fine chemicals and pharmaceuticals. The present work aims to establish the principles underlying the activity and selectivity of the enzyme through a combined computational, structural, and kinetic study using the substrate trans-stilbene oxide as a model system. Extensive empirical valence bond simulations have been performed on the wild-type enzyme together with several experimentally characterized mutants. We are able to computationally reproduce the differences between the activities of different stereoisomers of the substrate and the effects of mutations of several active-site residues. In addition, our results indicate the involvement of a previously neglected residue, H104, which is electrostatically linked to the general base H300. We find that this residue, which is highly conserved in epoxide hydrolases and related hydrolytic enzymes, needs to be in its protonated form in order to provide charge balance in an otherwise negatively charged active site. Our data show that unless the active-site charge balance is correctly treated in simulations, it is not possible to generate a physically meaningful model for the enzyme that can accurately reproduce activity and selectivity trends. We also expand our understanding of other catalytic residues, demonstrating in particular the role of a noncanonical residue, E35, as a "backup base" in the absence of H300. Our results provide a detailed view of the main factors driving catalysis and regioselectivity in this enzyme and identify targets for subsequent enzyme design efforts.

Is Promiscuous CALB a Good Scaffold for Designing New Epoxidases?

Candida Antarctica lipase B (CALB) is a well-known enzyme, especially because of its promiscuous activity. Due to its properties, CALB was widely used as a benchmark for designing new catalysts for important organic reactions. The active site of CALB is very similar to that of soluble epoxide hydrolase (sEH) formed by a nucleophile-histidine-acid catalytic triad and an oxyanion hole typical for molecular structures derived from processes of α/β hydrolases. In this work we are exploring these similarities and proposing a Ser105Asp variant of CALB as a new catalyst for epoxide hydrolysis. In particular, the hydrolysis of the trans-diphenylpropene oxide (t-DPPO) is studied by means of quantum cluster models mimicking the active site of both enzymes. Our results, based on semi-empirical and DFT calculations, suggest that mutant Ser105Asp CALB is a good protein scaffold to be used for the bio-synthesis of chiral compounds.

Modeling of interactions between xenobiotics and cytochrome P450 (CYP) enzymes

The adverse effects to humans and environment of only few chemicals are well known. Absorption, distribution, metabolism, and excretion (ADME) are the steps of pharmaco/toxicokinetics that determine the internal dose of chemicals to which the organism is exposed. Of all the xenobiotic-metabolizing enzymes, the cytochrome P450 (CYP) enzymes are the most important due to their abundance and versatility. Reactions catalyzed by CYPs usually turn xenobiotics to harmless and excretable metabolites, but sometimes an innocuous xenobiotic is transformed into a toxic metabolite. Data on ADME and toxicity properties of compounds are increasingly generated using in vitro and modeling (in silico) tools. Both physics-based and empirical modeling approaches are used. Numerous ligand-based and target-based as well as combined modeling methods have been employed to evaluate determinants of CYP ligand binding as well as predicting sites of metabolism and inhibition characteristics of test molecules. In silico prediction of CYP–ligand interactions have made crucial contributions in understanding (1) determinants of CYP ligand binding recognition and affinity; (2) prediction of likely metabolites from substrates; (3) prediction of inhibitors and their inhibition potency. Truly predictive models of toxic outcomes cannot be created without incorporating metabolic characteristics; in silico methods help producing such information and filling gaps in experimentally derived data. Currently modeling methods are not mature enough to replace standard in vitro and in vivo approaches, but they are already used as an important component in risk assessment of drugs and other chemicals.

Predicting drug metabolism: experiment and/or computation?

Drug metabolism can produce metabolites with physicochemical and pharmacological properties that differ substantially from those of the parent drug, and consequently has important implications for both drug safety and efficacy. To reduce the risk of costly clinical-stage attrition due to the metabolic characteristics of drug candidates, there is a need for efficient and reliable ways to predict drug metabolism in vitro, in silico and in vivo. In this Perspective, we provide an overview of the state of the art of experimental and computational approaches for investigating drug metabolism. We highlight the scope and limitations of these methods, and indicate strategies to harvest the synergies that result from combining measurement and prediction of drug metabolism.

In vitro inhibitory effects of ethanol extract of Danshen (Salvia miltiorrhiza) and its components on the catalytic activity of soluble epoxide hydrolase

BACKGROUND

Soluble epoxide hydrolase (sEH) has been demonstrated to be a key enzyme involved in the pathologic development of several cardiovascular diseases and inflammation, and inhibition of sEH is therefore very helpful or crucial for the treatment of ischemia-reperfusion injury, cardiac hypertrophy, hypertension and inflammation. Danshen, the dried root of Salvia miltiorrhiza (Fam. Labiatae), has been used for the treatment of cardiovascular and cerebrovascular diseases in China and other countries for hundreds of years. Recent studies indicated that Danshen and its preparations also have potential for the management of inflammation. However, little information is available about the possibility of Danshen and its components on sEH inhibition.

PURPOSE AND METHODS

Danshen extracts and its constituents were tested for sEH inhibition using its physiological substrate, 8,9-EET, based on a LC-MS/MS assay in this study.

RESULTS

Among the tested 15 compounds, tanshinone IIA and cryptotanshinone were found to be the potent (Ki = 0.87 μM) and medium (Ki = 6.7 μM) mixed-type inhibitors of sEH, respectively. Salvianolic acid C (Ki = 8.6 μM) was proved to be a moderate noncompetitive sEH inhibitor. In consistent with the inhibition results of the pure compounds, the 75% ethanol extract of Danshen (EE, IC50 = 86.5 μg/ml) which contained more tanshinone IIA and cryptotanshinone exhibited more potent inhibition on sEH than the water extract (WE, IC50 > 200 μg/ml) or 1 M NaHCO3 (BE, IC50 > 200 μg/ml) extract.

CONCLUSION

These data indicated that using the ethanol fraction of Danshen and increasing the amounts of tanshinone IIA, cryptotanshinone and salvianolic acid C, especially the contents of tanshinone IIA in Danshen extract or preparations to enhance the inhibitory effects on sEH might be efficient ways to improve its cardiovascular protective and anti-inflammatory effects, and that herbal medicines could be an untapped reservoir for sEH-inhibition agents and developing sEH inhibitors from the cardiovascular protective and anti-inflammatory herbs is a promising approach.

High-level QM/MM calculations support the concerted mechanism for Michael addition and covalent complex formation in thymidylate synthase

Thymidylate synthase (TS) is a promising cancer target, due to its crucial function in thymine synthesis. It performs the reductive methylation of 2'-deoxyuridine-5'-phosphate (dUMP) to thymidine-5'-phosphate (dTMP), using N-5,10-methylene-5,6,7,8-tetrahydrofolate (mTHF) as a cofactor. After the formation of the dUMP/mTHF/TS noncovalent complex, and subsequent conformational activation, this complex has been proposed to react via nucleophilic attack (Michael addition) by Cys146, followed by methylene-bridge formation to generate the ternary covalent intermediate. Herein, QM/MM (B3LYP-D/6-31+G(d)-CHARMM27) methods are used to model the formation of the ternary covalent intermediate. A two-dimensional potential energy surface reveals that the methylene-bridged intermediate is formed via a concerted mechanism, as indicated by a single transition state on the minimum energy pathway and the absence of a stable enolate intermediate. A range of different QM methods (B3LYP, MP2 and SCS-MP2, and different basis sets) are tested for the calculation of the activation energy barrier for the formation of the methylene-bridged intermediate. We test convergence of the QM/MM results with respect to size of the QM region. Inclusion of Arg166, which interacts with the nucleophilic thiolate, in the QM region is important for reliable results; the MM model apparently does not reproduce energies for distortion of the guanidinium side chain correctly. The spin component scaled-Møller-Plessett perturbation theory (SCS-MP2) approach was shown to be in best agreement (within 1.1 kcal/mol) while the results obtained with MP2 and B3LYP also yielded acceptable values (deviating by less than 3 kcal/mol) compared with the barrier derived from experiment. Our results indicate that using a dispersion-corrected DFT method, or a QM method with an accurate treatment of electron correlation, increases the agreement between the calculated and experimental activation energy barriers, compared with the semiempirical AM1 method. These calculations provide important insight into the reaction mechanism of TS and may be useful in the design of new TS inhibitors.

Recent advances in QM/MM free energy calculations using reference potentials

Background

Recent years have seen enormous progress in the development of methods for modeling (bio)molecular systems. This has allowed for the simulation of ever larger and more complex systems. However, as such complexity increases, the requirements needed for these models to be accurate and physically meaningful become more and more difficult to fulfill. The use of simplified models to describe complex biological systems has long been shown to be an effective way to overcome some of the limitations associated with this computational cost in a rational way.

Scope of review

Hybrid QM/MM approaches have rapidly become one of the most popular computational tools for studying chemical reactivity in biomolecular systems. However, the high cost involved in performing high-level QM calculations has limited the applicability of these approaches when calculating free energies of chemical processes. In this review, we present some of the advances in using reference potentials and mean field approximations to accelerate high-level QM/MM calculations. We present illustrative applications of these approaches and discuss challenges and future perspectives for the field.

Major conclusions

The use of physically-based simplifications has shown to effectively reduce the cost of high-level QM/MM calculations. In particular, lower-level reference potentials enable one to reduce the cost of expensive free energy calculations, thus expanding the scope of problems that can be addressed.

General significance

As was already demonstrated 40 years ago, the usage of simplified models still allows one to obtain cutting edge results with substantially reduced computational cost. This article is part of a Special Issue entitled Recent developments of molecular dynamics.

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We present some of the advances to accelerate high-level QM/MM calculations.

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Quantitative limitations of low-level methods can be overcome by these approaches.

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Reference potentials make free energy simulations feasible for large systems.

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Automated fitting reduces the need of expensive sampling of high-level approaches.

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Application of reference potentials can be extended to a wide range of processes.

A multiscale approach to modelling drug metabolism by membrane-bound cytochrome P450 enzymes

Cytochrome P450 enzymes are found in all life forms. P450s play an important role in drug metabolism, and have potential uses as biocatalysts. Human P450s are membrane-bound proteins. However, the interactions between P450s and their membrane environment are not well-understood. To date, all P450 crystal structures have been obtained from engineered proteins, from which the transmembrane helix was absent. A significant number of computational studies have been performed on P450s, but the majority of these have been performed on the solubilised forms of P450s. Here we present a multiscale approach for modelling P450s, spanning from coarse-grained and atomistic molecular dynamics simulations to reaction modelling using hybrid quantum mechanics/molecular mechanics (QM/MM) methods. To our knowledge, this is the first application of such an integrated multiscale approach to modelling of a membrane-bound enzyme. We have applied this protocol to a key human P450 involved in drug metabolism: CYP3A4. A biologically realistic model of CYP3A4, complete with its transmembrane helix and a membrane, has been constructed and characterised. The dynamics of this complex have been studied, and the oxidation of the anticoagulant R-warfarin has been modelled in the active site. Calculations have also been performed on the soluble form of the enzyme in aqueous solution. Important differences are observed between the membrane and solution systems, most notably for the gating residues and channels that control access to the active site. The protocol that we describe here is applicable to other membrane-bound enzymes.

Computing the Free Energy Barriers for Less by Sampling with a Coarse Reference Potential while Retaining Accuracy of the Target Fine Model

Proposed in this contribution is a protocol for calculating fine-physics (e.g., ab initio QM/MM) free-energy surfaces at a high level of accuracy locally (e.g., only at reactants and at the transition state for computing the activation barrier) from targeted fine-physics sampling and extensive exploratory coarse-physics sampling. The full free-energy surface is still computed but at a lower level of accuracy from coarse-physics sampling. The method is analytically derived in terms of the umbrella sampling and the free-energy perturbation methods which are combined with the thermodynamic cycle and the targeted sampling strategy of the paradynamics approach. The algorithm starts by computing low-accuracy fine-physics free-energy surfaces from the coarse-physics sampling in order to identify the reaction path and to select regions for targeted sampling. Thus, the algorithm does not rely on the coarse-physics minimum free-energy reaction path. Next, segments of high-accuracy free-energy surface are computed locally at selected regions from the targeted fine-physics sampling and are positioned relative to the coarse-physics free-energy shifts. The positioning is done by averaging the free-energy perturbations computed with multistep linear response approximation method. This method is analytically shown to provide results of the thermodynamic integration and the free-energy interpolation methods, while being extremely simple in implementation. Incorporating the metadynamics sampling to the algorithm is also briefly outlined. The application is demonstrated by calculating the B3LYP//6-31G*/MM free-energy barrier for an enzymatic reaction using a semiempirical PM6/MM reference potential. These modifications allow computing the activation free energies at a significantly reduced computational cost but at the same level of accuracy compared to computing full potential of mean force.

QM/MM free-energy simulations of reaction in Serratia marcescens Chitinase B reveal the protonation state of Asp142 and the critical role of Tyr214

Serratia marcescens Chitinase B (ChiB), belonging to the glycosidase family 18 (GH18), catalyzes the hydrolysis of β-1,4-glycosidic bond, with retention of configuration, via an unusual substrate-assisted mechanism, in which the substrate itself acts as an intramolecular nucleophile. Here, both elementary steps (glycosylation and deglycosylation) of the ChiB-catalyzed reaction are investigated by means of combined quantum mechanics/molecular mechanics (QM/MM) umbrella sampling molecular dynamics (MD) simulations at the SCC-DFTB/CHARMM22 level of theory. We examine the influence of the Asp142 protonation state on the reaction and the role that this residue performs in the reaction. Our simulations show that reaction with a neutral Asp142 is preferred and demonstrate that this residue provides electrostatic stabilization of the oxazolinium ion intermediate formed in the reaction. Insight into the conformational itinerary ((1,4)B↔(4)H5↔(4)C1) adopted by the substrate (bound in subsite -1) along the preferred reaction pathway is also provided by the simulations. The relative energies of the stationary points found along the reaction pathway calculated with SCC-DFTB and B3LYP were compared. The results suggest that SCC-DFTB is an accurate method for estimating the relative barriers for both steps of the reaction; however, it was found to overestimate the relative energy of an intermediate formed in the reaction when compared with the higher level of theory. Glycosylation is suggested to be a rate-determining step in the reaction with calculated overall reaction free-energy barrier of 20.5 kcal/mol, in a reasonable agreement with the 16.1 kcal/mol barrier derived from the experiment. The role of Tyr214 in catalysis was also investigated with the results, indicating that the residue plays a critical role in the deglycosylation step of the reaction. Simulations of the enzyme-product complex were also performed with an unbinding event suggested to have been observed, affording potential new mechanistic insight into the release of the product of ChiB.

Multiscale Free Energy Simulations: An Efficient Method for Connecting Classical MD Simulations to QM or QM/MM Free Energies Using Non-Boltzmann Bennett Reweighting Schemes

The reliability of free energy simulations (FES) is limited by two factors: (a) the need for correct sampling and (b) the accuracy of the computational method employed. Classical methods (e.g., force fields) are typically used for FES and present a myriad of challenges, with parametrization being a principle one. On the other hand, parameter-free quantum mechanical (QM) methods tend to be too computationally expensive for adequate sampling. One widely used approach is a combination of methods, where the free energy difference between the two end states is computed by, e.g., molecular mechanics (MM), and the end states are corrected by more accurate methods, such as QM or hybrid QM/MM techniques. Here we report two new approaches that significantly improve the aforementioned scheme; with a focus on how to compute corrections between, e.g., the MM and the more accurate QM calculations. First, a molecular dynamics trajectory that properly samples relevant conformational degrees of freedom is generated. Next, potential energies of each trajectory frame are generated with a QM or QM/MM Hamiltonian. Free energy differences are then calculated based on the QM or QM/MM energies using either a non-Boltzmann Bennett approach (QM-NBB) or non-Boltzmann free energy perturbation (NB-FEP). Both approaches are applied to calculate relative and absolute solvation free energies in explicit and implicit solvent environments. Solvation free energy differences (relative and absolute) between ethane and methanol in explicit solvent are used as the initial test case for QM-NBB. Next, implicit solvent methods are employed in conjunction with both QM-NBB and NB-FEP to compute absolute solvation free energies for 21 compounds. These compounds range from small molecules such as ethane and methanol to fairly large, flexible solutes, such as triacetyl glycerol. Several technical aspects were investigated. Ultimately some best practices are suggested for improving methods that seek to connect MM to QM (or QM/MM) levels of theory in FES.

Quantum mechanics/molecular mechanics modeling of regioselectivity of drug metabolism in cytochrome P450 2C9

Cytochrome P450 enzymes (P450s) are important in drug metabolism and have been linked to adverse drug reactions. P450s display broad substrate reactivity, and prediction of metabolites is complex. QM/MM studies of P450 reactivity have provided insight into important details of the reaction mechanisms and have the potential to make predictions of metabolite formation. Here we present a comprehensive study of the oxidation of three widely used pharmaceutical compounds (S-ibuprofen, diclofenac, and S-warfarin) by one of the major drug-metabolizing P450 isoforms, CYP2C9. The reaction barriers to substrate oxidation by the iron-oxo species (Compound I) have been calculated at the B3LYP-D/CHARMM27 level for different possible metabolism sites for each drug, on multiple pathways. In the cases of ibuprofen and warfarin, the process with the lowest activation energy is consistent with the experimentally preferred metabolite. For diclofenac, the pathway leading to the experimentally observed metabolite is not the one with the lowest activation energy. This apparent inconsistency with experiment might be explained by the two very different binding modes involved in oxidation at the two competing positions. The carboxylate of diclofenac interacts strongly with the CYP2C9 Arg108 side chain in the transition state for formation of the observed metabolite—but not in that for the competing pathway. We compare reaction barriers calculated both in the presence and in the absence of the protein and observe a marked improvement in selectivity prediction ability upon inclusion of the protein for all of the substrates studied. The barriers calculated with the protein are generally higher than those calculated in the gas phase. This suggests that active-site residues surrounding the substrate play an important role in controlling selectivity in CYP2C9. The results show that inclusion of sampling (particularly) and dispersion effects is important in making accurate predictions of drug metabolism selectivity of P450s using QM/MM methods.

Combined quantum mechanics/molecular mechanics (QM/MM) methods in computational enzymology

Computational enzymology is a rapidly maturing field that is increasingly integral to understanding mechanisms of enzyme-catalyzed reactions and their practical applications. Combined quantum mechanics/molecular mechanics (QM/MM) methods are important in this field. By treating the reacting species with a quantum mechanical method (i.e., a method that calculates the electronic structure of the active site) and including the enzyme environment with simpler molecular mechanical methods, enzyme reactions can be modeled. Here, we review QM/MM methods and their application to enzyme-catalyzed reactions to investigate fundamental and practical problems in enzymology. A range of QM/MM methods is available, from cheaper and more approximate methods, which can be used for molecular dynamics simulations, to highly accurate electronic structure methods. We discuss how modeling of reactions using such methods can provide detailed insight into enzyme mechanisms and illustrate this by reviewing some recent applications. We outline some practical considerations for such simulations. Further, we highlight applications that show how QM/MM methods can contribute to the practical development and application of enzymology, e.g., in the interpretation and prediction of the effects of mutagenesis and in drug and catalyst design.

Why nature really chose phosphate

Phosphoryl transfer plays key roles in signaling, energy transduction, protein synthesis, and maintaining the integrity of the genetic material. On the surface, it would appear to be a simple nucleophile displacement reaction. However, this simplicity is deceptive, as, even in aqueous solution, the low-lying d-orbitals on the phosphorus atom allow for eight distinct mechanistic possibilities, before even introducing the complexities of the enzyme catalyzed reactions. To further complicate matters, while powerful, traditional experimental techniques such as the use of linear free-energy relationships (LFER) or measuring isotope effects cannot make unique distinctions between different potential mechanisms. A quarter of a century has passed since Westheimer wrote his seminal review, 'Why Nature Chose Phosphate' (Science 235 (1987), 1173), and a lot has changed in the field since then. The present review revisits this biologically crucial issue, exploring both relevant enzymatic systems as well as the corresponding chemistry in aqueous solution, and demonstrating that the only way key questions in this field are likely to be resolved is through careful theoretical studies (which of course should be able to reproduce all relevant experimental data). Finally, we demonstrate that the reason that nature really chose phosphate is due to interplay between two counteracting effects: on the one hand, phosphates are negatively charged and the resulting charge-charge repulsion with the attacking nucleophile contributes to the very high barrier for hydrolysis, making phosphate esters among the most inert compounds known. However, biology is not only about reducing the barrier to unfavorable chemical reactions. That is, the same charge-charge repulsion that makes phosphate ester hydrolysis so unfavorable also makes it possible to regulate, by exploiting the electrostatics. This means that phosphate ester hydrolysis can not only be turned on, but also be turned off, by fine tuning the electrostatic environment and the present review demonstrates numerous examples where this is the case. Without this capacity for regulation, it would be impossible to have for instance a signaling or metabolic cascade, where the action of each participant is determined by the fine-tuned activity of the previous piece in the production line. This makes phosphate esters the ideal compounds to facilitate life as we know it.

Computational protein engineering: bridging the gap between rational design and laboratory evolution

Enzymes are tremendously proficient catalysts, which can be used as extracellular catalysts for a whole host of processes, from chemical synthesis to the generation of novel biofuels. For them to be more amenable to the needs of biotechnology, however, it is often necessary to be able to manipulate their physico-chemical properties in an efficient and streamlined manner, and, ideally, to be able to train them to catalyze completely new reactions. Recent years have seen an explosion of interest in different approaches to achieve this, both in the laboratory, and in silico. There remains, however, a gap between current approaches to computational enzyme design, which have primarily focused on the early stages of the design process, and laboratory evolution, which is an extremely powerful tool for enzyme redesign, but will always be limited by the vastness of sequence space combined with the low frequency for desirable mutations. This review discusses different approaches towards computational enzyme design and demonstrates how combining newly developed screening approaches that can rapidly predict potential mutation “hotspots” with approaches that can quantitatively and reliably dissect the catalytic step can bridge the gap that currently exists between computational enzyme design and laboratory evolution studies.

Obtaining optical purity for product diols in enzyme-catalyzed epoxide hydrolysis: contributions from changes in both enantio- and regioselectivity

Enzyme variants of the plant epoxide hydrolase StEH1 displaying improved stereoselectivities in the catalyzed hydrolysis of (2,3-epoxypropyl)benzene were generated by directed evolution. The evolution was driven by iterative saturation mutagenesis in combination with enzyme activity screenings where product chirality was the decisive selection criterion. Analysis of the underlying causes of the increased diol product ratios revealed two major contributing factors: increased enantioselectivity for the corresponding epoxide enantiomer(s) and, in some cases, a concomitant change in regioselectivity in the catalyzed epoxide ring-opening half-reaction. Thus, variant enzymes that catalyzed the hydrolysis of racemic (2,3-epoxypropyl)benzene into the R-diol product in an enantioconvergent manner were isolated.

Effects of Dispersion in Density Functional Based Quantum Mechanical/Molecular Mechanical Calculations on Cytochrome P450 Catalyzed Reactions

Density functional theory (DFT) based quantum mechanical/molecular mechanical (QM/MM) calculations have provided valuable insight into the reactivity of the cytochrome P450 family of enzymes (P450s). A failure of commonly used DFT methods, such as B3LYP, is the neglect of dispersion interactions. An empirical dispersion correction has been shown to improve the accuracy of gas phase DFT calculations of P450s. The current work examines the effect of the dispersion correction in QM/MM calculations on P450s. The hydrogen abstraction from camphor, and hydrogen abstraction and C-O addition of cyclohexene and propene by P450cam have been modeled, along with the addition of benzene to Compound I in CYP2C9, at the B3LYP-D2/CHARMM27 level of theory. Single point energy calculations were also performed at the B3LYP-D3//B3LYP-D2/CHARMM27 level. The dispersion corrections lower activation energy barriers significantly (by ∼5 kcal/mol), as seen for gas phase calculations, but has a small effect on optimized geometries.These effects are likely to be important in modeling reactions catalyzed by other enzymes also. Given the low computational cost of including such dispersion corrections, we recommend doing so in all B3LYP based QM/MM calculations.

Exploring, refining, and validating the paradynamics QM/MM sampling

The performance of the paradynamics (PD) reference potential approach in QM/MM calculations is examined. It is also clarified that, in contrast to some possible misunderstandings, this approach provides a rigorous strategy for QM/MM free energy calculations. In particular, the PD approach provides a gradual and controlled way of improving the evaluation of the free energy perturbation associated with moving from the EVB reference potential to the target QM/MM surface. This is achieved by moving from the linear response approximation to the full free energy perturbation approach in evaluating the free energy changes. We also present a systematic way of improving the reference potential by using Gaussian-based correction potentials along a reaction coordinate. In parallel, we review other recent adaptations of the reference potential approach, emphasizing and demonstrating the advantage of using the EVB potential as a reference potential, relative to semiempirical QM/MM molecular orbital potentials. We also compare the PD results to those obtained by direct calculations of the potentials of the mean force (PMF). Additionally, we propose a way of accelerating the PMF calculations by using Gaussian-based negative potentials along the reaction coordinate (which are also used in the PD refinement). Finally, we discuss performance of the PD and the metadynamics approaches in ab initio QM/MM calculations and emphasize the advantage of using the PD approach.

Convergence of QM/MM free-energy perturbations based on molecular-mechanics or semiempirical simulations

Lately, there has been great interest in performing free-energy perturbation (FEP) at the combined quantum mechanics and molecular mechanics (QM/MM) level, e.g. for enzyme reactions. Such calculations require extensive sampling of phase space, which typically is prohibitive with density-functional theory or ab initio methods. Therefore, such calculations have mostly been performed with semiempirical QM (SQM) methods, or by using a thermodynamic cycle involving sampling at the MM level and perturbations between the MM and QM/MM levels of theory. However, the latter perturbations typically have convergence problems, unless the QM system is kept fixed during the simulations, because the MM and QM/MM descriptions of the internal degrees of freedom inside the QM system are too dissimilar. We have studied whether the convergence of the MM → QM/MM perturbation can be improved by using a thoroughly parameterised force field or by using SQM/MM methods. As a test case we use the first half-reaction of haloalkane dehalogenase and the QM calculations are performed with the PBE, B3LYP, and TPSSH density-functional methods. We show that the convergence can be improved with a tailored force field, but only locally around the parameterised state. Simulations based on SQM/MM methods using the MNDO, AM1, PM3, RM1, PDDG-MNDO, and PDDG-PM3 Hamiltonians have slightly better convergence properties, but very long simulations are still needed (~10 ns) and convergence is obtained only if electrostatic interactions between the QM system and the surroundings are ignored. This casts some doubts on the common practice to base QM/MM FEPs on semiempirical simulations without any reweighting of the trajectories.