Transition state theory can be used in studies of enzyme catalysis: lessons from simulations of tunnelling and dynamical effects in lipoxygenase and other systems

Nanoscale chemical reaction exploration with a quantum magnifying glass

Nanoscopic systems exhibit diverse molecular substructures by which they facilitate specific functions. Theoretical models of them, which aim at describing, understanding, and predicting these capabilities, are difficult to build. Viable quantum-classical hybrid models come with specific challenges regarding atomistic structure construction and quantum region selection. Moreover, if their dynamics are mapped onto a state-to-state mechanism such as a chemical reaction network, its exhaustive exploration will be impossible due to the combinatorial explosion of the reaction space. Here, we introduce a "quantum magnifying glass" that allows one to interactively manipulate nanoscale structures at the quantum level. The quantum magnifying glass seamlessly combines autonomous model parametrization, ultra-fast quantum mechanical calculations, and automated reaction exploration. It represents an approach to investigate complex reaction sequences in a physically consistent manner with unprecedented effortlessness in real time. We demonstrate these features for reactions in bio-macromolecules and metal-organic frameworks, diverse systems that highlight general applicability.

Antioxidant activity of lidocaine, bupivacaine, and ropivacaine in aqueous and lipophilic environments: an experimental and computational study

Introduction: Local anesthetics are widely recognized pharmaceutical compounds with various clinical effects. Recent research indicates that they positively impact the antioxidant system and they may function as free radical scavengers. We hypothesize that their scavenging activity is influenced by the lipophilicity of the environment. Methods: We assessed the free radical scavenging capacity of three local anesthetics (lidocaine, bupivacaine, and ropivacaine) using ABTS, DPPH, and FRAP antioxidant assays. We also employed quantum chemistry methods to find the most probable reaction mechanism. The experiments were conducted in an aqueous environment simulating extracellular fluid or cytosol, and in a lipophilic environment (n-octanol) simulating cellular membranes or myelin sheets. Results: All local anesthetics demonstrated ABTS˙⁺ radical scavenging activity, with lidocaine being the most effective. Compared to Vitamin C, lidocaine exhibited a 200-fold higher half-maximal inhibitory concentration. The most thermodynamically favorable and only possible reaction mechanism involved hydrogen atom transfer between the free radical and the -C-H vicinal to the carbonyl group. We found that the antioxidant activity of all tested local anesthetics was negligible in lipophilic environments, which was further confirmed by quantum chemical calculations. Conclusion: Local anesthetics exhibit modest free radical scavenging activity in aqueous environments, with lidocaine demonstrating the highest activity. However, their antioxidant activity in lipophilic environments, such as cellular membranes, myelin sheets, and adipose tissue, appears to be negligible. Our results thus show that free radical scavenging activity is influenced by the lipophilicity of the environment.

Current Status of the X + C2H6 [X ≡ H, F(2P), Cl(2P), O(3P), OH] Hydrogen Abstraction Reactions: A Theoretical Review

This paper is a detailed review of the chemistry of medium-size reactive systems using the following hydrogen abstraction reactions with ethane, X + C₂H₆ → HX + C₂H₅; X ≡ H, F(²P), Cl(²P), O(³P) and OH, and focusing attention mainly on the theoretical developments. These bimolecular reactions range from exothermic to endothermic systems and from barrierless to high classical barriers of activation. Thus, the topography of the reactive systems changes from reaction to reaction with the presence or not of stabilized intermediate complexes in the entrance and exit channels. The review begins with some reflections on the inherent problems in the theory/experiment comparison. When one compares kinetics or dynamics theoretical results with experimental measures, one is testing both the potential energy surface describing the nuclei motion and the kinetics or dynamics method used. Discrepancies in the comparison may be due to inaccuracies of the surface, limitations of the kinetics or dynamics methods, and experimental uncertainties that also cannot be ruled out. The paper continues with a detailed review of some bimolecular reactions with ethane, beginning with the reactions with hydrogen atoms. The reactions with halogens present a challenge owing to the presence of stabilized intermediate complexes in the entrance and exit channels and the influence of the spin-orbit states on reactivity. Reactions with O(³P) atoms lead to three surfaces, which is an additional difficulty in the theoretical study. Finally, the reactions with the hydroxyl radical correspond to a reactive system with ten atoms and twenty-four degrees of freedom. Throughout this review, different strategies in the development of analytical potential energy surfaces describing these bimolecular reactions have been critically analyzed, showing their advantages and limitations. These surfaces are fitted to a large number of ab initio calculations, and we found that a huge number of calculations leads to accurate surfaces, but this information does not guarantee that the kinetics and dynamics results match the experimental measurements.

Structural dynamics support electrostatic interactions in the active site of Adenylate Kinase

Electrostatic preorganization as well as structural and dynamic heterogeneity are often used to rationalize the remarkable catalytic efficiency of enzymes. However, they are often presented as incompatible because the generation of permanent electrostatic effects implies that the protein structure remains rigid. Here, we use a metric, electric fields, that can treat electrostatic contributions and dynamics effects on equal footing, for a unique perspective on enzymatic catalysis. We find that the residues that contribute the most to electrostatic interactions with the substrate in the active site of Adenylate Kinase (our working example) are also the most flexible residues. Further, entropy-tuning mutations raise flexibility at the picosecond timescale where more conformations can be visited on short time periods, thereby softening the sharp heterogeneity normally visible at the microsecond timescale.

Why Monoamine Oxidase B Preferably Metabolizes N-Methylhistamine over Histamine: Evidence from the Multiscale Simulation of the Rate-Limiting Step

Histamine levels in the human brain are controlled by rather peculiar metabolic pathways. In the first step, histamine is enzymatically methylated at its imidazole N^τ atom, and the produced N-methylhistamine undergoes an oxidative deamination catalyzed by monoamine oxidase B (MAO-B), as is common with other monoaminergic neurotransmitters and neuromodulators of the central nervous system. The fact that histamine requires such a conversion prior to oxidative deamination is intriguing since MAO-B is known to be relatively promiscuous towards monoaminergic substrates; its in-vitro oxidation of N-methylhistamine is about 10 times faster than that for histamine, yet this rather subtle difference appears to be governing the decomposition pathway. This work clarifies the MAO-B selectivity toward histamine and N-methylhistamine by multiscale simulations of the rate-limiting hydride abstraction step for both compounds in the gas phase, in aqueous solution, and in the enzyme, using the established empirical valence bond methodology, assisted by gas-phase density functional theory (DFT) calculations. The computed barriers are in very good agreement with experimental kinetic data, especially for relative trends among systems, thereby reproducing the observed MAO-B selectivity. Simulations clearly demonstrate that solvation effects govern the reactivity, both in aqueous solution as well as in the enzyme although with an opposing effect on the free energy barrier. In the aqueous solution, the transition-state structure involving histamine is better solvated than its methylated analog, leading to a lower barrier for histamine oxidation. In the enzyme, the higher hydrophobicity of N-methylhistamine results in a decreased number of water molecules at the active side, leading to decreased dielectric shielding of the preorganized catalytic electrostatic environment provided by the enzyme. This renders the catalytic environment more efficient for N-methylhistamine, giving rise to a lower barrier relative to histamine. In addition, the transition state involving N-methylhistamine appears to be stabilized by the surrounding nonpolar residues to a larger extent than with unsubstituted histamine, contributing to a lower barrier with the former.

Dipole Moment Variation Clears Up Electronic Excitations in the π-Stacked Complexes of Fluorescent Protein Chromophores

We propose a quantitative structure-property relationship (QSPR) model for prediction of spectral tuning in cyan, green, orange, and red fluorescent proteins, which are engineered by motifs of the green fluorescent protein. Protein variants, in which their chromophores are involved in the π-stacking interaction with amino acid residues tyrosine, phenylalanine, and histidine, are prospective markers useful in bioimaging and super-resolution microscopy. In this work, we constructed training sets of the π-stacked complexes of four fluorescent protein chromophores (of the green, orange, red, and cyan series) with various substituted benzenes and imidazoles and tested the use of dipole moment variation upon excitation (DMV) as a descriptor to evaluate the vertical excitation energies in these systems. To validate this approach, we computed and analyzed electron density distributions of the π-stacked complexes and correlated the QSPR predictions with the reference values of the transition energies obtained using the high-level ab initio quantum chemistry methods. According to our results, the use of the DMV descriptor allows one to predict excitation energies in the π-stacked complexes with errors not exceeding 0.1 eV, which makes this model a practically useful tool in the development of efficient fluorescent markers for in vivo imaging.

A comparison of the hydrogen bond interaction dynamics in the adenine and thymine crystals: BOMD and spectroscopic study

In this work we present the comparison study of Adenine and Thymine crystals based on the hydrogen bond dynamics. The ab initio molecular dynamics have been used as the base for the further studied interactions observed inside crystals. The generated power spectra, as well as the fluctuation of the interaction energies, showed large differences between hydrogen bond networks in the considered crystals. The analysis of intermolecular interactions have been done base on the reactivity descriptors as well frontiers orbitals along trajectories. The main results showed that in adenine crystals the intermolecular interactions have three directions and fluctuate, while in the thymine crystal have only two directions and are weak but stable. These results explain also on the difference between adenine and thymine melting temperature.

Exploring Reactive Conformations of Coenzyme A during Binding and Unbinding to Pyruvate Formate-Lyase

Pyruvate formate-lyase (PFL) is a glycyl radical enzyme that converts pyruvate and coenzyme A (CoA) into formate and acetyl-CoA in two half-reactions. Recently, we showed that the acetylation of the PFL active site in the first half-reaction induces subtle conformational changes, leading to the opening of a potential channel for CoA entry. Entry of CoA into the active site is crucial for the second half-reaction, involving the acetyl transfer to CoA, and the completion of the catalytic cycle. Using steered molecular dynamics (SMD) simulations, performed on acetylated and nonacetylated monomeric PFL model systems, we first of all investigate the possible entry/exit pathways of CoA with respect to the active site through the previously identified channel. We then perform umbrella sampling simulations on multiple snapshots from SMD trajectories as well as unrestrained molecular dynamics simulations starting from the final structures obtained from entry SMD, with a view to identifying possible bound states of CoA in the near vicinity of the active site. Detailed study of the unrestrained dissociation processes reveals the presence of stable and reactive bound states of CoA close to the active site, one of which is in an ideal position for triggering the second half-reaction. Examination of the spatial distributions associated with the reactive bound states allows us to discuss the free energy barriers. Umbrella sampling, performed on snapshots from unrestrained dynamics confirms the above findings. The significance of the results for the catalysis are discussed for both acetylated and nonacetylated systems.

Quantum Suppression of Intramolecular Deuterium Kinetic Isotope Effects in a Pericyclic Hydrogen Transfer Reaction

It is generally accepted that hydrogen tunneling enhances both primary and secondary H/D kinetic isotope effects (KIEs) over what would be expected under the assumptions of classical barrier transition. Previous studies have exclusively shown that the effects of tunneling upon primary H/D KIEs have been much larger than those observed for secondary H/D KIEs. Here we present a series of experimental H/D KIE results associated with the Chugaev elimination of methyl xanthate derived from β-phenylethanol over the temperature range of 180 to 290 °C. Intramolecular H/D KIEs computed according to classical transition state theory (TST) are markedly overestimated relative to experimentally measured values. Experimental intermolecular H/D KIEs and direct dynamic calculations based on canonical variational transition state theory (CVT) with small-curvature tunneling correction (SCT) reveal that this result is largely the consequence of extraordinary tunneling enhancement of the secondary H/D KIE. This unexpected behavior is examined in the context of other similar hydrogen transfer reactions.

Proton tunnelling in hydrogen bonds and its implications in an induced-fit model of enzyme catalysis

The role of proton tunnelling in biological catalysis is investigated here within the frameworks of quantum information theory and thermodynamics. We consider the quantum correlations generated through two hydrogen bonds between a substrate and a prototypical enzyme that first catalyses the tautomerization of the substrate to move on to a subsequent catalysis, and discuss how the enzyme can derive its catalytic potency from these correlations. In particular, we show that classical changes induced in the binding site of the enzyme spreads the quantum correlations among all of the four hydrogen-bonded atoms thanks to the directionality of hydrogen bonds. If the enzyme rapidly returns to its initial state after the binding stage, the substrate ends in a new transition state corresponding to a quantum superposition. Open quantum system dynamics can then naturally drive the reaction in the forward direction from the major tautomeric form to the minor tautomeric form without needing any additional catalytic activity. We find that in this scenario the enzyme lowers the activation energy so much that there is no energy barrier left in the tautomerization, even if the quantum correlations quickly decay.

Uncertainty quantification for quantum chemical models of complex reaction networks

For the quantitative understanding of complex chemical reaction mechanisms, it is, in general, necessary to accurately determine the corresponding free energy surface and to solve the resulting continuous-time reaction rate equations for a continuous state space. For a general (complex) reaction network, it is computationally hard to fulfill these two requirements. However, it is possible to approximately address these challenges in a physically consistent way. On the one hand, it may be sufficient to consider approximate free energies if a reliable uncertainty measure can be provided. On the other hand, a highly resolved time evolution may not be necessary to still determine quantitative fluxes in a reaction network if one is interested in specific time scales. In this paper, we present discrete-time kinetic simulations in discrete state space taking free energy uncertainties into account. The method builds upon thermo-chemical data obtained from electronic structure calculations in a condensed-phase model. Our kinetic approach supports the analysis of general reaction networks spanning multiple time scales, which is here demonstrated for the example of the formose reaction. An important application of our approach is the detection of regions in a reaction network which require further investigation, given the uncertainties introduced by both approximate electronic structure methods and kinetic models. Such cases can then be studied in greater detail with more sophisticated first-principles calculations and kinetic simulations.

Fundamental Insights into Proton-Coupled Electron Transfer in Soybean Lipoxygenase from Quantum Mechanical/Molecular Mechanical Free Energy Simulations

The proton-coupled electron transfer (PCET) reaction catalyzed by soybean lipoxygenase has served as a prototype for understanding hydrogen tunneling in enzymes. Herein this PCET reaction is studied with mixed quantum mechanical/molecular mechanical (QM/MM) free energy simulations. The free energy surfaces are computed as functions of the proton donor-acceptor (C-O) distance and the proton coordinate, and the potential of mean force is computed as a function of the C-O distance, inherently including anharmonicity. The simulation results are used to calculate the kinetic isotope effects for the wild-type enzyme (WT) and the L546A/L754A double mutant (DM), which have been measured experimentally to be ∼80 and ∼700, respectively. The PCET reaction is found to be exoergic for WT and slightly endoergic for the DM, and the equilibrium C-O distance for the reactant is found to be ∼0.2 Å greater for the DM than for WT. The larger equilibrium distance for the DM, which is due mainly to less optimal substrate binding in the expanded binding cavity, is primarily responsible for its higher kinetic isotope effect. The calculated potentials of mean force are anharmonic and relatively soft at shorter C-O distances, allowing efficient thermal sampling of the shorter distances required for effective hydrogen tunneling. The primarily local electrostatic field at the transferring hydrogen is ∼100 MV/cm in the direction to facilitate proton transfer and increases dramatically as the C-O distance decreases. These simulations suggest that the overall protein environment is important for conformational sampling of active substrate configurations aligned for proton transfer, but the PCET reaction is influenced primarily by local electrostatic effects that facilitate conformational sampling of shorter proton donor-acceptor distances required for effective hydrogen tunneling.

Why does the Y326I mutant of monoamine oxidase B decompose an endogenous amphetamine at a slower rate than the wild type enzyme? Reaction step elucidated by multiscale molecular simulations

This work investigates the Y326I point mutation effect on the kinetics of oxidative deamination of phenylethylamine (PEA) catalyzed by the monoamine oxidase B (MAO B) enzyme. PEA is a neuromodulator capable of affecting the plasticity of the brain and is responsible for the mood enhancing effect caused by physical exercise. Due to a similar functionality, PEA is often regarded as an endogenous amphetamine. The rate limiting step of the deamination was simulated at the multiscale level, employing the Empirical Valence Bond approach for the quantum treatment of the involved valence states, whereas the environment (solvated protein) was represented with a classical force field. A comparison of the reaction free energy profiles delivered by simulation of the reaction in the wild type MAO B and its Y326I mutant yields an increase in the barrier by 1.06 kcal mol^-1 upon mutation, corresponding to a roughly 6-fold decrease in the reaction rate. This is in excellent agreement with the experimental kinetic studies. Inspection of simulation trajectories reveals possible sources of the point mutation effect, namely vanishing favorable electrostatic interactions between PEA and a Tyr326 side chain and an increased amount of water molecules at the active site due to the replacement of tyrosine by a less spacious isoleucine residue, thereby increasing the dielectric shielding of the catalytic environment provided by the enzyme.

Witnessing eigenstates for quantum simulation of Hamiltonian spectra

The efficient calculation of Hamiltonian spectra, a problem often intractable on classical machines, can find application in many fields, from physics to chemistry. We introduce the concept of an "eigenstate witness" and, through it, provide a new quantum approach that combines variational methods and phase estimation to approximate eigenvalues for both ground and excited states. This protocol is experimentally verified on a programmable silicon quantum photonic chip, a mass-manufacturable platform, which embeds entangled state generation, arbitrary controlled unitary operations, and projective measurements. Both ground and excited states are experimentally found with fidelities >99%, and their eigenvalues are estimated with 32 bits of precision. We also investigate and discuss the scalability of the approach and study its performance through numerical simulations of more complex Hamiltonians. This result shows promising progress toward quantum chemistry on quantum computers.

Novel electrochemical route to cleaner fuel dimethyl ether

Methanol, the simplest alcohol, and dimethyl ether, the simplest ether, are central compounds in the search for alternative “green” combustion fuels. In fact, they are generally considered as the cornerstones of the envisaged “Methanol Economy” scenario, as they are able to efficiently produce energy in an environmentally friendly manner. However, despite a massive amount of research in this field, the synthesis of dimethyl ether from liquid methanol has never so far been reported. Here we present a computational study, based on ab initio Molecular Dynamics, which suggests a novel synthesis route to methanol dehydration – leading thus to the dimethyl ether synthesis – through the application of strong electric fields. Besides proving the impressive catalytic effects afforded by the field, our calculations indicate that the obtained dimethyl ether is stable and that it can be progressively accumulated thanks to the peculiar chemical pathways characterising the methanol reaction network under electric field. These results suggest that the experimental synthesis of dimethyl ether from liquid methanol could be achieved, possibly in the proximity of field emitter tips.

Elucidating reaction mechanisms on quantum computers

With rapid recent advances in quantum technology, we are close to the threshold of quantum devices whose computational powers can exceed those of classical supercomputers. Here, we show that a quantum computer can be used to elucidate reaction mechanisms in complex chemical systems, using the open problem of biological nitrogen fixation in nitrogenase as an example. We discuss how quantum computers can augment classical computer simulations used to probe these reaction mechanisms, to significantly increase their accuracy and enable hitherto intractable simulations. Our resource estimates show that, even when taking into account the substantial overhead of quantum error correction, and the need to compile into discrete gate sets, the necessary computations can be performed in reasonable time on small quantum computers. Our results demonstrate that quantum computers will be able to tackle important problems in chemistry without requiring exorbitant resources.

Modeling covalent-modifier drugs

In this review, we present a summary of how computer modeling has been used in the development of covalent-modifier drugs. Covalent-modifier drugs bind by forming a chemical bond with their target. This covalent binding can improve the selectivity of the drug for a target with complementary reactivity and result in increased binding affinities due to the strength of the covalent bond formed. In some cases, this results in irreversible inhibition of the target, but some targeted covalent inhibitor (TCI) drugs bind covalently but reversibly. Computer modeling is widely used in drug discovery, but different computational methods must be used to model covalent modifiers because of the chemical bonds formed. Structural and bioinformatic analysis has identified sites of modification that could yield selectivity for a chosen target. Docking methods, which are used to rank binding poses of large sets of inhibitors, have been augmented to support the formation of protein-ligand bonds and are now capable of predicting the binding pose of covalent modifiers accurately. The pK_a's of amino acids can be calculated in order to assess their reactivity towards electrophiles. QM/MM methods have been used to model the reaction mechanisms of covalent modification. The continued development of these tools will allow computation to aid in the development of new covalent-modifier drugs. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman.

Perspective: Defining and quantifying the role of dynamics in enzyme catalysis

Enzymes control chemical reactions that are key to life processes, and allow them to take place on the time scale needed for synchronization between the relevant reaction cycles. In addition to general interest in their biological roles, these proteins present a fundamental scientific puzzle, since the origin of their tremendous catalytic power is still unclear. While many different hypotheses have been put forward to rationalize this, one of the proposals that has become particularly popular in recent years is the idea that dynamical effects contribute to catalysis. Here, we present a critical review of the dynamical idea, considering all reasonable definitions of what does and does not qualify as a dynamical effect. We demonstrate that no dynamical effect (according to these definitions) has ever been experimentally shown to contribute to catalysis. Furthermore, the existence of non-negligible dynamical contributions to catalysis is not supported by consistent theoretical studies. Our review is aimed, in part, at readers with a background in chemical physics and biophysics, and illustrates that despite a substantial body of experimental effort, there has not yet been any study that consistently established a connection between an enzyme's conformational dynamics and a significant increase in the catalytic contribution of the chemical step. We also make the point that the dynamical proposal is not a semantic issue but a well-defined scientific hypothesis with well-defined conclusions.

Complete sampling of an enzyme reaction pathway: a lesson from gas phase simulations

With proper sampling strategy, convergence of free energy profiles of biomolecular reactions in the gas phase can be achieved in microseconds of simulation.

Insights into enzyme point mutation effect by molecular simulation: phenylethylamine oxidation catalyzed by monoamine oxidase A

The I335Y point mutation effect on the kinetics of phenylethylamine decomposition catalyzed by monoamine oxidase A was elucidated by means of molecular simulation. The established empirical valence bond methodology was used in conjunction with the free energy perturbation sampling technique and a classical force field representing the state of reactants and products. The methodology allows for the simulation of chemical reactions, in the present case the breaking of the α-C-H bond in a phenylethylamine substrate and the subsequent hydrogen transfer to the flavin cofactor, resulting in the formation of the N-H bond on flavin. The empirical parameters were calibrated against the experimental data for the simulated reaction in a wild type protein and then used for the calculation of the reaction free energy profile in the I335Y mutant. In very good agreement with the measured kinetic data, mutation increases the free energy barrier for the rate limiting step by slightly more than 1 kcal mol(-1) and consequently decreases the rate constant by about an order of magnitude. The magnitude of the computed effect slightly varies with simulation settings, but always remains in reasonable agreement with the experiment. Analysis of trajectories reveals a major change in the interaction between phenyl rings of the substrate and the neighboring Phe352 residue upon the I335Y mutation due to the increased local polarity, leading to an attenuated quadrupole interaction between the rings and destabilization of the transition state. Additionally, the increased local polarity in the mutant allows for a larger number of water molecules to be present near the active site, effectively shielding the catalytic effect of the enzyme and contributing to the increased barrier.

The Importance of the MM Environment and the Selection of the QM Method in QM/MM Calculations: Applications to Enzymatic Reactions

In this chapter, we discuss the influence of an anisotropic protein environment on the reaction mechanisms of saccharopine reductase and uroporphyrinogen decarboxylase, respectively, via the use of a quantum mechanical and molecular mechanical (QM/MM) approach. In addition, we discuss the importance of selecting a suitable DFT functional to be used in a QM/MM study of a key intermediate in the mechanism of 8R-lipoxygenase, a nonheme iron enzyme. In the case of saccharopine reductase, while the enzyme utilizes a substrate-assisted catalytic pathway, it was found that only through treating the polarizing effect of the active site, via the use of an electronic embedding formalism, was agreement with experimental kinetic data obtained. Similarly, in the case of uroporphyrinogen decarboxylase, the effect of the protein environment on the catalytic mechanism was found to be such that the calculated rate-limiting barrier is in good agreement with related experimentally determined values for the first decarboxylation of the substrate. For 8R-lipoxygenase, it was found that the geometries and energies of the multicentered open-shell intermediate complexes formed during the mechanism are quite sensitive to the choice of the density functional theory method. Thus, while density functional theory has become the method of choice in QM/MM studies, care must be taken in the selection of a particular high-level method.

Nuclear quantum tunnelling in enzymatic reactions – an enzymologist's perspective

The roles of nuclear quantum tunnelling and dynamics in enzyme reactions are discussed in this perspective on H-transfer reactions.

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.

Hydrogen donor-acceptor fluctuations from kinetic isotope effects: a phenomenological model

Kinetic isotope effects (KIEs) and their temperature dependence can probe the structural and dynamic nature of enzyme-catalyzed proton or hydride transfers. The molecular interpretation of their temperature dependence requires expensive and specialized quantum mechanics/molecular mechanics (QM/MM) calculations to provide a quantitative molecular understanding. Currently available phenomenological models use a nonadiabatic assumption that is not appropriate for most hydride and proton-transfer reactions, while others require more parameters than the experimental data justify. Here we propose a phenomenological interpretation of KIEs based on a simple method to quantitatively link the size and temperature dependence of KIEs to a conformational distribution of the catalyzed reaction. This model assumes adiabatic hydrogen tunneling, and by fitting experimental KIE data, the model yields a population distribution for fluctuations of the distance between donor and acceptor atoms. Fits to data from a variety of proton and hydride transfers catalyzed by enzymes and their mutants, as well as nonenzymatic reactions, reveal that steeply temperature-dependent KIEs indicate the presence of at least two distinct conformational populations, each with different kinetic behaviors. We present the results of these calculations for several published cases and discuss how the predictions of the calculations might be experimentally tested. This analysis does not replace molecular QM/MM investigations, but it provides a fast and accessible way to quantitatively interpret KIEs in the context of a Marcus-like model.

Collective Reaction Coordinate for Hybrid Quantum and Molecular Mechanics Simulations: A Case Study of the Hydride Transfer in Dihydrofolate Reductase

The optimal description of the reaction coordinate in chemical systems is of great importance in simulating condensed phase reactions. In the current work, we present a collective reaction coordinate which is composed of several geometric coordinates which represent structural progress during the course of a hydride transfer reaction: the antisymmetric reactive stretch coordinate, the donor-acceptor distance (DAD) coordinate, and an orbital rehybridization coordinate. In this approach, the former coordinate serves as a distinguished reaction coordinate, while the latter two serve as environmental, Marcus-type inner-sphere reorganization coordinates. The classical free energy surface is obtained from multidimensional quantum mechanics-molecular mechanics (QM/MM) potential of mean force (PMF) simulations in conjunction with a general and efficient multidimensional weighted histogram method implementation. The minimum free energy path, or the collective reaction coordinate, connecting the dividing hypersurface to reactants and products, is obtained using an iterative scheme. In this approach, the string method is used to find the minimum free energy path. This path guides the multidimensional sampling, while the path is adaptively refined until convergence is achieved. As a model system, we choose the hydride transfer reaction in Escherichia coli dihydrofolate reductase (ecDHFR) using a recently developed accurate semiempirical potential energy surface. To estimate the advantages of the collective reaction coordinate, we perform activated dynamics simulations to obtain the reaction transmission coefficient. The results show that the combination of a distinguished reaction coordinate and an inner-sphere reorganization coordinate considerably reduces the dividing surface recrossing.

Car-Parrinello simulation of the vibrational spectrum of a medium strong hydrogen bond by two-dimensional quantization of the nuclear motion: application to 2-hydroxy-5-nitrobenzamide

The nature of medium strong intra- and intermolecular hydrogen bonding in 2-hydroxy-5-nitrobenzamide in the crystal phase was examined by infrared spectroscopy and Car-Parrinello molecular dynamics simulation. The focal point of our study was the part of the infrared spectra associated with the O-H and N-H stretching modes that are very sensitive to the strength of hydrogen bonding. For spectra calculations we used an isolated dimer and the fully periodic crystal environment. We calculated the spectra by using harmonic approximation, the time course of the dipole moment function as obtained from the Car-Parrinello simulation, and the quantization of the nuclear motion of the proton for an instantaneous snapshot of the structures in one and two dimensions. Although quantitative assessment of the agreement between the computed and experimental band contour is difficult due to the fact that the experimental band is very broad, we feel that the most reasonable qualitative agreement with the experiment is obtained from snapshot structures and two-dimensional quantization of the proton motion. We have also critically examined the methods of constructing the one-dimensional proton potential. Perspectives are given for the treatment of nuclear quantum effects in biocatalysis.

Proton-transport mechanisms in cytochrome c oxidase revealed by studies of kinetic isotope effects

Cytochrome c oxidase (CytcO) is a membrane-bound enzyme, which catalyzes the reduction of di-oxygen to water and uses a major part of the free energy released in this reaction to pump protons across the membrane. In the Rhodobacter sphaeroides aa₃ CytcO all protons that are pumped across the membrane, as well as one half of the protons that are used for O₂ reduction, are transferred through one specific intraprotein proton pathway, which holds a highly conserved Glu286 residue. Key questions that need to be addressed in order to understand the function of CytcO at a molecular level are related to the timing of proton transfers from Glu286 to a "pump site" and the catalytic site, respectively. Here, we have investigated the temperature dependencies of the H/D kinetic-isotope effects of intramolecular proton-transfer reactions in the wild-type CytcO as well as in two structural CytcO variants, one in which proton uptake from solution is delayed and one in which proton pumping is uncoupled from O₂ reduction. These processes were studied for two specific reaction steps linked to transmembrane proton pumping, one that involves only proton transfer (peroxy-ferryl, P→F, transition) and one in which the same sequence of proton transfers is also linked to electron transfer to the catalytic site (ferryl-oxidized, F→O, transition). An analysis of these reactions in the framework of theory indicates that that the simpler, P→F reaction is rate-limited by proton transfer from Glu286 to the catalytic site. When the same proton-transfer events are also linked to electron transfer to the catalytic site (F→O), the proton-transfer reactions might well be gated by a protein structural change, which presumably ensures that the proton-pumping stoichiometry is maintained also in the presence of a transmembrane electrochemical gradient. Furthermore, the present study indicates that a careful analysis of the temperature dependence of the isotope effect should help us in gaining mechanistic insights about CytcO.

Transmission coefficients for chemical reactions with multiple states: role of quantum decoherence

Transition-state theory (TST) is a widely accepted paradigm for rationalizing the kinetics of chemical reactions involving one potential energy surface (PES). Multiple PES reaction rate constants can also be estimated within semiclassical approaches provided the hopping probability between the quantum states is taken into account when determining the transmission coefficient. In the Marcus theory of electron transfer, this hopping probability was historically calculated with models such as Landau-Zener theory. Although the hopping probability is intimately related to the question of the transition from the fully quantum to the semiclassical description, this issue is not adequately handled in physicochemical models commonly in use. In particular, quantum nuclear effects such as decoherence or dephasing are not present in the rate constant expressions. Retaining the convenient semiclassical picture, we include these effects through the introduction of a phenomenological quantum decoherence function. A simple modification to the usual TST rate constant expression is proposed: in addition to the electronic coupling, a characteristic decoherence time τ(dec) now also appears as a key parameter of the rate constant. This new parameter captures the idea that molecular systems, although intrinsically obeying quantum mechanical laws, behave semiclassically after a finite but nonzero amount of time (τ(dec)). This new degree of freedom allows a fresh look at the underlying physics of chemical reactions involving more than one quantum state. The ability of the proposed formula to describe the main physical lines of the phenomenon is confirmed by comparison with results obtained from density functional theory molecular dynamics simulations for a triplet to singlet transition within a copper dioxygen adduct relevant to the question of dioxygen activation by copper monooxygenases.

Spontaneous proton transfer to a conserved intein residue determines on-pathway protein splicing

The discovery of inteins, which are protein-splicing elements, has stimulated interest for various applications in chemical biology, bioseparations, drug delivery, and sensor development. However, for inteins to effectively contribute to these applications, an increased mechanistic understanding of cleavage and splicing reactions is required. While the multistep chemical reaction that leads to splicing is often explored and utilized, it is not clear how the intein navigates through the reaction space. The sequence of reaction steps must progress in concert in order to yield efficient splicing while minimizing off-pathway cleavage reactions. In this study, we demonstrate that formation of a previously identified branched intermediate is the critical step for determining splicing over cleavage products. By combining experimental assays and quantum mechanical simulations, we identify the electrostatic interactions that are important to the dynamics of the reaction steps. We illustrate, via an animated simulation trajectory, a proton transfer from the first C-terminal extein residue to a conserved aspartate, which synchronizes the multistep enzymatic reaction that is key to splicing. This work provides new insights into the complex interplay between critical active-site residues in the protein splicing mechanism, thereby facilitating biotechnological application while shedding light on multistep enzyme activity.