Environmentally coupled hydrogen tunneling. Linking catalysis to dynamics.

Many biological C-H activation reactions exhibit nonclassical kinetic isotope effects (KIEs). These nonclassical KIEs are too large (kH/kD > 7) and/or exhibit unusual temperature dependence such that the Arrhenius prefactor KIEs (AH/AD) fall outside of the semiclassical range near unity. The focus of this minireview is to discuss such KIEs within the context of the environmentally coupled hydrogen tunneling model. Full tunneling models of hydrogen transfer assume that protein or solvent fluctuations generate a reactive configuration along the classical, heavy-atom coordinate, from which the hydrogen transfers via nuclear tunneling. Environmentally coupled tunneling also invokes an environmental vibration (gating) that modulates the tunneling barrier, leading to a temperature-dependent KIE. These properties directly link enzyme fluctuations to the reaction coordinate for hydrogen transfer, making a quantum view of hydrogen transfer necessarily a dynamic view of catalysis. The environmentally coupled hydrogen tunneling model leads to a range of magnitudes of KIEs, which reflect the tunneling barrier, and a range of AH/AD values, which reflect the extent to which gating modulates hydrogen transfer. Gating is the primary determinant of the temperature dependence of the KIE within this model, providing insight into the importance of this motion in modulating the reaction coordinate. The potential use of variable temperature KIEs as a direct probe of coupling between environmental dynamics and the reaction coordinate is described. The evolution from application of a tunneling correction to a full tunneling model in enzymatic H transfer reactions is discussed in the context of a thermophilic alcohol dehydrogenase and soybean lipoxygenase-1.     

A new conceptual framework for enzyme catalysis. Hydrogen tunnelling coupled to enzyme dynamics in flavoprotein and quinoprotein enzymes.

Recent years have witnessed high levels of activity in identifying enzyme systems that catalyse H-transfer by quantum tunneling. Rather than being restricted to a small number of specific enzymes as perceived initially, it has now become an accepted mechanism for H-transfer in a growing number of enzymes. Furthermore, H-tunneling is driven by the thermally induced dynamics of the enzyme. In some of those enzymes that break stable C-H bonds the reaction proceeds purely by quantum tunneling, without the need to partially ascend the barrier. Enzymes studied that fall into this category include the flavoprotein and quinoprotein amine dehydrogenases, which have proved to be excellent model systems. These enzymes have enabled us to study the relationship between barrier shape and reaction kinetics. This has involved studies with "slow" and "fast" substrates and enzymes impaired by mutagenesis. A number of key questions now remain, including the nature of the coupling between protein dynamics and quantum tunneling. The wide-ranging implications of quantum tunneling introduce a paradigm shift in the conceptual framework for enzyme catalysis, inhibition and design.     

Structural bases of hydrogen tunneling in enzymes: progress and puzzles

Accumulating experimental evidence suggests that the occurrence of hydrogen tunneling is likely to be widespread in enzyme-catalyzed reactions. The realization that hydrogen can transfer via tunneling mechanisms has far-reaching implications for our understanding of enzyme catalysis involving proton, hydride or hydrogen atom transfer reactions. The current status of the field is highlighted by three enzyme systems that have been under intensive study in recent years, including soybean lipoxygenase-1, thermophilic alcohol dehydrogenase and dihydrofolate reductase. Particular attention has been devoted to the issues of whether protein dynamics modulate hydrogen tunneling probability and whether the tunneling process contributes to the catalytic power of enzymes.     

H-transfers in Photosystem II: what can we learn from recent lessons in the enzyme community?

Over the last 10 years, studies of enzyme systems have demonstrated that, in many cases, H-transfers occur by a quantum mechanical tunneling mechanism analogous to long-range electron transfer. H-transfer reactions can be described by an extension of Marcus theory and, by substituting hydrogen with deuterium (or even tritium), it is possible to explore this theory in new ways by employing kinetic isotope effects. Because hydrogen has a relatively short deBroglie wavelength, H-transfers are controlled by the width of the reaction barrier. By coupling protein dynamics to the reaction coordinate, enzymes have the potential ability to facilitate more efficient H-tunneling by modulating barrier properties. In this review, we describe recent advances in both experimental and theoretical studies of enzymatic H-transfer, in particular the role of protein dynamics or promoting motions. We then discuss possible consequences with regard to tyrosine oxidation/reduction kinetics in Photosystem II.     

Br?nsted-Evans-Polanyi relationships for C–C bond forming and C–C bond breaking reactions in thiamine-catalyzed decarboxylation of 2-keto acids using density functional theory

The concept of generalized enzyme reactions suggests that a wide variety of substrates can undergo enzymatic transformations, including those whose biotransformation has not yet been realized. The use of quantum chemistry to evaluate kinetic feasibility is an attractive approach to identify enzymes for the proposed transformation. However, the sheer number of novel transformations that can be generated makes this impractical as a screening approach. Therefore, it is essential to develop structure/activity relationships based on quantities that are more efficient to calculate. In this work, we propose a structure/activity relationship based on the free energy of binding or reaction of non-native substrates to evaluate the catalysis relative to that of native substrates. While Br?nsted-Evans-Polanyi (BEP) relationships such as that proposed here have found broad application in heterogeneous catalysis, their extension to enzymatic catalysis is limited. We report here on density functional theory (DFT) studies for C–C bond formation and C–C bond cleavage associated with the decarboxylation of six 2-keto acids by a thiamine-containing enzyme (EC 1.2.7.1) and demonstrate a linear relationship between the free energy of reaction and the activation barrier. We then applied this relationship to predict the activation barriers of 17 chemically similar novel reactions. These calculations reveal that there is a clear correlation between the free energy of formation of the transition state and the free energy of the reaction, suggesting that this method can be further extended to predict the kinetics of novel reactions through our computational framework for discovery of novel biochemical transformations.     

Short-strong hydrogen bonds and a low barrier transition state for the proton transfer reaction in RNase A catalysis: a quantum chemical study

There is growing evidence that some enzymes catalyze reactions through the formation of short-strong hydrogen bonds as first suggested by Gerlt and Gassman. Support comes from several experimental and quantum chemical studies that include correlation energies on model systems. In the present study, the process of proton transfer between hydroxyl and imidazole groups, a model of the crucial step in the hydrolysis of RNA by the enzymes of the RNase A family, is investigated at the quantum mechanical level of density functional theory and perturbation theory at the MP2 level. The model focuses on the nature of the formation of a complex between the important residues of the protein and the hydroxyl group of the substrate. We have also investigated different configurations of the ground state that are important in the proton transfer reaction. The nature of bonding between the catalytic unit of the enzyme and the substrate in the model is investigated by Bader's atoms in molecule theory. The contributions of solvation and vibrational energies corresponding to the reactant, the transition state and the product configurations are also evaluated. Furthermore, the effect of protein environment is investigated by considering the catalytic unit surrounded by complete proteins--RNase A and Angiogenin. The results, in general, indicate the formation of a short-strong hydrogen bond and the formation of a low barrier transition state for the proton transfer model of the enzyme.     

pH-dependent redox potential: how to use it correctly in the activation energy analysis

The activation barrier (the activation free energy) for the reaction's elementary act proper does not depend on the presence of reactants outside the reaction complex. The barrier is determined directly by the concentration-independent configurational free energy. In the case of redox reactants with pH-dependent redox potential, only the pH-independent quantity, the configurational redox potential enters immediately into expression for activation energy. Some typical cases of such reactions have been discussed (e.g., simultaneous proton and electron detachment, acid dissociation followed by oxidation, dissociation after oxidation, and others). For these mechanisms, the algorithms for calculation of the configurational redox potential from the experimentally determined redox potentials have been described both for the data related to a dissolved reactant or to a prosthetic group of an enzyme. Some examples of pH-dependent enzymatic redox reactions, in particular for the Rieske iron-sulfur protein, have been discussed.     

pH-dependent redox potential: how to use it correctly in the activation energy analysis

The activation barrier (the activation free energy) for the reaction's elementary act proper does not depend on the presence of reactants outside the reaction complex. The barrier is determined directly by the concentration-independent configurational free energy. In the case of redox reactants with pH-dependent redox potential, only the pH-independent quantity, the configurational redox potential enters immediately into expression for activation energy. Some typical cases of such reactions have been discussed (e.g., simultaneous proton and electron detachment, acid dissociation followed by oxidation, dissociation after oxidation, and others). For these mechanisms, the algorithms for calculation of the configurational redox potential from the experimentally determined redox potentials have been described both for the data related to a dissolved reactant or to a prosthetic group of an enzyme. Some examples of pH-dependent enzymatic redox reactions, in particular for the Rieske iron-sulfur protein, have been discussed.     

The catalytic effect of dihydrofolate reductase and its mutants is determined by reorganization energies

The effect of distant mutations on the catalytic reaction of dihydrofolate reductase (DHFR) is reexamined by empirical valence bond simulations. The simulations reproduce for the first time the changes in the observed rate constants (without the use of adjustable parameters for this purpose) and show that the changes in activation barriers are strongly correlated with the corresponding changes in the reorganization energy. The preorganization of the polar groups of enzymes is the key catalytic factor, and anticatalytic mutations destroy this preorganization. Some anticatalytic mutations in DHFR also increase the distance between the donor and acceptor, but this effect is not directly related to catalysis since the native enzyme and the uncatalyzed reaction in water have similar average donor-acceptor distances. Insight into the effect of a mutation is provided by constructing the relevant free energy surfaces in terms of the generalized solute-solvent coordinates. It is shown how the mutations change the reaction coordinate and the activation barrier, and it is clarified that the corresponding changes do not reflect dynamical effects. It is also pointed out that all reactions in a condensed phase involve correlated motions (both in enzymes and in solution) and that the change of such motions upon mutations is a result of the change in the shape of the multidimensional reaction path on the solute-solvent surface, rather than the reason for the change in rate constant. Thus, as far as catalysis is concerned, the change in the activation barrier is due to the change in the electrostatic preorganization energy.     

Properties of intramolecular proton transfer in carbonic anhydrase III.

We investigated the efficiency of glutamic acid 64 and aspartic acid 64 as proton donors to the zinc-bound hydroxide in a series of site-specific mutants of human carbonic anhydrase III (HCA III). Rate constants for this intramolecular proton transfer, a step in the catalyzed dehydration of bicarbonate, were determined from the proton-transfer-dependent rates of release of H2 18O from the enzyme measured by mass spectrometry. The free energy plots representing these rate constants could be fit by the Marcus rate theory, resulting in an intrinsic barrier for the proton transfer of deltaG0++ = 2.2 +/- 0.5 kcal/mol, and a work function or thermodynamic contribution to the free energy of reaction wr = 10.8 +/- 0.1 kcal/mol. These values are very similar in magnitude to the Marcus parameters describing intramolecular proton transfer from His64 and His67 to the zinc-bound hydroxide in mutants of HCA III. That result and the equivalent efficiency of Glu64 and Asp64 as proton donors in the catalysis by CA III demonstrate a lack of specificity in proton transfer from these sites, which is indirect evidence of a number of proton conduction pathways through different structures of intervening water chains. The dominance of the thermodynamic contribution or work function for all of these proton transfers is consistent with the view that formation and breaking of hydrogen bonds in such water chains is a limiting factor for proton translocation.     

Reduction of intrinsic kinetic and thermodynamic barriers for enzyme-catalysed proton transfers from carbon acid substrates

Many enzymes catalyse the heterolytic abstraction of the alpha-proton from a carbon acid substrate. Gerlt and Gassman have applied Marcus formalism to such proton transfer reactions to argue that transition states for concerted general acid-general base catalysed enolization at enzyme active sites occur late on the reaction coordinate (J. Am. Chem. Soc. 115 (1993) 11552). We postulate that as an enzyme evolves, it may decrease deltaG++ for a proton transfer step associated with substrate enolization by following the path of steepest descent on the two-dimensional surface corresponding to deltaG++, as defined by Marcus formalism. We show that for an enzyme that has decreased deltaG++ following the path of steepest descent, the values of the intrinsic kinetic (deltaG++(int,E)) and thermodynamic (deltaG(E)0) barriers for proton transfer reactions on the enzyme may be predicted from the known values of deltaG++(int,N) and deltaG(N)0 for the corresponding non-enzymic reaction and the free energy of activation on the enzyme (deltaG++(E)). In addition, the enzymic transition state will occur later on the reaction coordinate than the corresponding non-enzymic transition state (i.e. x++(E)>x++(N)) if the condition (6 - square root 2)/82deltaG++(int,N).     

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

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

Insight into the phosphodiesterase mechanism from combined QM/MM free energy simulations

Molecular dynamics simulations employing a combined quantum mechanical and molecular mechanical potential have been carried out to elucidate the reaction mechanism of the hydrolysis of a cyclic nucleotide cAMP substrate by phosphodiesterase 4B (PDE4B). PDE4B is a member of the PDE superfamily of enzymes that play crucial roles in cellular signal transduction. We have determined a two-dimensional potential of mean force (PMF) for the coupled phosphoryl bond cleavage and proton transfer through a general acid catalysis mechanism in PDE4B. The results indicate that the ring-opening process takes place through an S(N)2 reaction mechanism, followed by a proton transfer to stabilize the leaving group. The computed free energy of activation for the PDE4B-catalyzed cAMP hydrolysis is about 13 kcal·mol(-1) and an overall reaction free energy is about -17 kcal·mol(-1), both in accord with experimental results. In comparison with the uncatalyzed reaction in water, the enzyme PDE4B provides a strong stabilization of the transition state, lowering the free energy barrier by 14 kcal·mol(-1). We found that the proton transfer from the general acid residue His234 to the O3' oxyanion of the ribosyl leaving group lags behind the nucleophilic attack, resulting in a shallow minimum on the free energy surface. A key contributing factor to transition state stabilization is the elongation of the distance between the divalent metal ions Zn(2+) and Mg(2+) in the active site as the reaction proceeds from the Michaelis complex to the transition state.     

Systematic optimization model and algorithm for binding sequence selection in computational enzyme design

A systematic optimization model for binding sequence selection in computational enzyme design was developed based on the transition state theory of enzyme catalysis and graph‐theoretical modeling. The saddle point on the free energy surface of the reaction system was represented by catalytic geometrical constraints, and the binding energy between the active site and transition state was minimized to reduce the activation energy barrier. The resulting hyperscale combinatorial optimization problem was tackled using a novel heuristic global optimization algorithm, which was inspired and tested by the protein core sequence selection problem. The sequence recapitulation tests on native active sites for two enzyme catalyzed hydrolytic reactions were applied to evaluate the predictive power of the design methodology. The results of the calculation show that most of the native binding sites can be successfully identified if the catalytic geometrical constraints and the structural motifs of the substrate are taken into account. Reliably predicting active site sequences may have significant implications for the creation of novel enzymes that are capable of catalyzing targeted chemical reactions.     

Density-functional investigation on the mechanism of H-atom abstraction by lipoxygenase

Using experimentally calibrated density functional calculations on models of the active site of soybean lipoxygenase 1 (SLO-1), insight has been obtained into the coordination flexibility of the iron active site and its molecular mechanism of catalysis. The ferrous form of SLO-1 shows a variation in coordination number in solution that is related to a weakly coordinating Asn694 ligand. From the calculations it is determined that the weak Fe-O(694) bond associated with this coordination flexibility is due to a sideways tilted geometry of Asn694 that is imposed on the site by the protein. Release of this constraint (by altering the hydrogen bonding network) leads to a pure six-coordinate site. In contrast, the ferric form of the enzyme stays five-coordinate. In this case, deprotonation of a coordinated water gives a strong hydroxo donor in the cis position to Asn694, weakening the Fe-O(694) bond. Hence, Asn694 is a stronger ligand to the reduced relative to the oxidized site. Using these experimentally calibrated models, the reaction energy for H-atom transfer in SLO-1 has been calculated to be about -18 kcal/mol. The observed change in coordination number going from five-coordinate in ferric to six-coordinate in ferrous SLO-1 increases the reduction potential of the iron active site. Hence, the protein adjusts the active site for optimal reactivity. Analysis of the electronic structure along the reaction coordinate shows that the H-atom transfer in SLO-1 actually corresponds to a proton-coupled electron transfer (PCET). The transferred electron does not localize on the proton, but tunnels directly from the substrate to the ferric active site in a concerted proton tunneling-electron tunneling (PTET) process. The covalently linked Fe-O-H-C bridge in the transition state lowers the energy barrier and provides an efficient superexchange pathway for this tunneling. The thermal barrier for the PTET process is estimated from the calculations to be about +15 kcal/mol including zero-point energy corrections. This corresponds to a thermal reaction rate of k(therm) approximately 1 s(-1). In comparison, the rate of proton tunneling can be as high as 2 x 10(9) s(-1) under these conditions.     

The role of tunneling in enzyme catalysis of C-H activation

Recent data from studies of enzyme catalyzed hydrogen transfer reactions implicate a new theoretical context in which to understand C-H activation. This is much closer to the Marcus theory of electron transfer, in that environmental factors influence the probability of effective wave function overlap from donor to acceptor atoms. The larger size of hydrogen and the availability of three isotopes (H, D and T) introduce a dimension to the kinetic analysis that is not available for electron transfer. This concerns the role of gating between donor and acceptor atoms, in particular whether the system in question is able to tune distance between reactants to achieve maximal tunneling efficiency. Analysis of enzyme systems is providing increasing evidence of a role for active site residues in optimizing the inter-nuclear distance for nuclear tunneling. The ease with which this optimization can be perturbed, through site-specific mutagenesis or an alteration in reaction conditions, is also readily apparent from an analysis of the changes in the temperature dependence of hydrogen isotope effects.     

The role of tunneling in enzyme catalysis of C-H activation

Recent data from studies of enzyme catalyzed hydrogen transfer reactions implicate a new theoretical context in which to understand C-H activation. This is much closer to the Marcus theory of electron transfer, in that environmental factors influence the probability of effective wave function overlap from donor to acceptor atoms. The larger size of hydrogen and the availability of three isotopes (H, D and T) introduce a dimension to the kinetic analysis that is not available for electron transfer. This concerns the role of gating between donor and acceptor atoms, in particular whether the system in question is able to tune distance between reactants to achieve maximal tunneling efficiency. Analysis of enzyme systems is providing increasing evidence of a role for active site residues in optimizing the inter-nuclear distance for nuclear tunneling. The ease with which this optimization can be perturbed, through site-specific mutagenesis or an alteration in reaction conditions, is also readily apparent from an analysis of the changes in the temperature dependence of hydrogen isotope effects.     

Charge delocalization in proton channels, I: the aquaporin channels and proton blockage

The explicit contribution to the free energy barrier and proton conductance from the delocalized nature of the excess proton is examined in aquaporin channels using an accurate all-atom molecular dynamics computer simulation model. In particular, the channel permeation free energy profiles are calculated and compared for both a delocalized (fully Grotthuss shuttling) proton and a classical (nonshuttling) hydronium ion along two aquaporin channels, Aqp1 and GlpF. To elucidate the effects of the bipolar field thought to arise from two alpha-helical macrodipoles on proton blockage, free energy profiles were also calculated for computational mutants of the two channels where the bipolar field was eliminated by artificially discharging the backbone atoms. Comparison of the free energy profiles between the proton and hydronium cases indicates that the magnitude of the free energy barrier and position of the barrier peak for the fully delocalized and shuttling proton are somewhat different from the case of the (localized) classical hydronium. The proton conductance through the two aquaporin channels is also estimated using Poisson-Nernst-Planck theory for both the Grotthuss shuttling excess proton and the classical hydronium cation.     

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 aa? CytcO all protons that are pumped across the membrane, as well as one half of the protons that are used for O? 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 O? 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.     

Proton tunneling and enzyme catalysis

Summary It is proposed in this paper that enzymes, by virtue of a number of correctly positioned sites of interaction with substrates, can force the compression of hydrogen bonds, increasing the probability of proton transfer by quantum mechanical tunneling. By such a catalytic mechanism a rate enhancement of many orders of magnitude may be obtained with a very low energy input requirement. The mechanism would, however, require a highly structured catalyst.Pertinent aspects of hydrogen bond theory and of tunneling theory are briefly reviewed.Work supported by NIGMS Training Grant No. GM 678-07.