Coupling of hydrogenic tunneling to active-site motion in the hydrogen radical transfer catalyzed by a coenzyme B12-dependent mutase

Role of Microsolvation and Quantum Effects in the Accurate Prediction of Kinetic Isotope Effects: The Case of Hydrogen Atom Abstraction in Ethanol by Atomic Hydrogen in Aqueous Solution

Hydrogen abstraction from ethanol by atomic hydrogen in aqueous solution is studied using two theoretical approaches: the multipath variational transition state theory (MP-VTST) and a path-integral formalism in combination with free-energy perturbation and umbrella sampling (PI-FEP/UM). The performance of the models is compared to experimental values of H kinetic isotope effects (KIE). Solvation models used in this study ranged from purely implicit, via mixed–microsolvation treated quantum mechanically via the density functional theory (DFT) to fully explicit representation of the solvent, which was incorporated using a combined quantum mechanical-molecular mechanical (QM/MM) potential. The effects of the transition state conformation and the position of microsolvating water molecules interacting with the solute on the KIE are discussed. The KIEs are in good agreement with experiment when MP-VTST is used together with a model that includes microsolvation of the polar part of ethanol by five or six water molecules, emphasizing the importance of explicit solvation in KIE calculations. Both, MP-VTST and PI-FEP/UM enable detailed characterization of nuclear quantum effects accompanying the hydrogen atom transfer reaction in aqueous solution.

Theoretical Study on the Dynamics and Kinetics of the Reaction of CH2OH with OH

The stochastic one-dimensional chemical master equation (CME) simulation method was used to investigate the dynamics of the reaction of CH₂OH with OH. A multiwell multichannel potential energy surface (PES) was constructed at the CCSD(T)/Aug-cc-pVTZ//CBS-QB3 and QCISD(T)/Aug-cc-pVTZ//CBS-QB3 levels of theory. The constructed PES consisted of three chemically activated intermediates and two van der Waals complexes. The fractional population analysis unraveled the role of the energized intermediates and van der Waals complexes in the early stages of this complex reaction. The CME calculations provided the phenomenological rate constants through analysis of the eigenvalues and eigenvectors of collision matrices while Leonard-Jones potential was used to model the collisions. The CME results indicated that CH₂O and H₂O were the major products, in accordance with the literature. Also, the findings declared the temperature and pressure independence of the reaction over a wide range of temperature (250 to 2400 K) and pressure (0.1 to 7 atm). Furthermore, the efficiency of tunneling on the hydrogen transfer isomerization reaction of trans-HCOH to CH₂O was confirmed over the temperature range of 250 to 3000 K. The rate constants for different reaction channels are reported.

Modeling the Reactions Catalyzed by Coenzyme B12 Dependent Enzymes: Accuracy and Cost-Quality Balance

The reactions catalyzed by coenzyme B₁₂ dependent enzymes are formally initiated by the homolytic cleavage of a carbon-cobalt bond and a subsequent or concerted H-atom-transfer reaction. A reasonable model chemistry for describing those reactions should, therefore, account for an accurate description of both reactions. The inherent limitation due to the necessary system size renders the coenzyme B₁₂ system a suitable candidate for DFT or hybrid QM/MM methods; however, the accurate description of both homolytic Co-C cleavage and H-atom-transfer reactions within this framework is challenging and can lead to controversial results with varying accuracy. We present an assessment study of 16 common density functionals applied to prototypical model systems for both reactions. H-abstraction reactions were modeled on the basis of four reference reactions designed to resemble a broad range of coenzyme B₁₂ reactions. The Co-C cleavage reaction is treated by an ONIOM(QM/MM) setup that is in excellent agreement with solution-phase experimental data and is as accurate as full DFT calculations on the complete model system. We find that the meta-GGAs TPSS-D3 and M06L-D3 and the meta-hybrid M06-D3 give the best overall performance with MUEs for both types of reactions below 10 kJ mol^-1. Our recommended model chemistry allows for a fast and accurate description of coenzyme B₁₂ chemistry that is readily applicable to study the reactions in an enzymatic framework.

Computational Prediction of Excited-State Carbon Tunneling in the Two Steps of Triplet Zimmerman Di-π-Methane Rearrangement

The photoinduced Zimmerman di-π-methane (DPM) rearrangement of polycyclic molecules to form synthetically useful cyclopropane derivatives was found experimentally to proceed in a triplet excited state. We have applied state-of-the-art quantum mechanical methods, including M06-2X, DLPNO-CCSD(T) and variational transition-state theory with multidimensional tunneling corrections, to an investigation of the reaction rates of the two steps in the triplet DPM rearrangement of dibenzobarrelene, benzobarrelene and barrelene. This study predicts a high probability of carbon tunneling in regions around the two consecutive transition states at 200-300 K, and an enhancement in the rates by 104-276/35-67% with carbon tunneling at 200/300 K. The Arrhenius plots of the rate constants were found to be curved at low temperatures. Moreover, the computed ¹²C/¹³C kinetic isotope effects were affected significantly by carbon tunneling and temperature. Our predictions of electronically excited-state carbon tunneling and two consecutive carbon tunneling are unprecedented. Heavy-atom tunneling in some photoinduced reactions with reactive intermediates and narrow barriers can be potentially observed at relatively low temperature in experiments.

Measurement of Enzyme Isotope Effects

Enzyme isotope effects, or the kinetic effects of "heavy" enzymes, refer to the effect of isotopically labeled protein residues on the enzyme's activity or physical properties. These effects are increasingly employed in the examination of the possible contributions of protein dynamics to enzyme catalysis. One hypothesis assumed that isotopic substitution of all ¹²C, ¹⁴N, and nonexchangeable ¹H by ¹³C, ¹⁵N, and ²H, would slow down protein picosecond to femtosecond dynamics without any effect on the system's electrostatics following the Born-Oppenheimer approximation. It was suggested that reduced reaction rates reported for several "heavy" enzymes accords with that hypothesis. However, numerous deviations from the predictions of that hypothesis were also reported. Current studies also attempt to test the role of individual residues by site-specific labeling or by labeling a pattern of residues on activity. It appears that in several systems the protein's fast dynamics are indeed reduced in "heavy" enzymes in a way that reduces the probability of barrier crossing of its chemical step. Other observations, however, indicated that slower protein dynamics are electrostatically altered in isotopically labeled enzymes. Interestingly, these effects appear to be system dependent, thus it might be premature to suggest a general role of "heavy" enzymes' effect on catalysis.

Enhanced Rigidification within a Double Mutant of Soybean Lipoxygenase Provides Experimental Support for Vibronically Nonadiabatic Proton-Coupled Electron Transfer Models

Soybean lipoxygenase (SLO) is a prototype for nonadiabatic hydrogen tunneling reactions and, as such, has served as the subject of numerous theoretical studies. In this work, we report a nearly temperature-independent kinetic isotope effect (KIE) with an average KIE value of 661 ± 27 for a double mutant (DM) of SLO at six temperatures. The data are well-reproduced within a vibronically nonadiabatic proton-coupled electron transfer model in which the active site has become rigidified compared to wild-type enzyme and single-site mutants. A combined temperature-pressure perturbation further shows that temperature-dependent global motions within DM-SLO are more resistant to perturbation by elevated pressure. These findings provide strong experimental support for the model of hydrogen tunneling in SLO, where optimization of both local protein and ligand motions and distal conformational rearrangements is a prerequisite for effective proton vibrational wave function overlap between the substrate and the active-site iron cofactor.

Variational transition state theory: theoretical framework and recent developments

This article reviews the fundamentals of variational transition state theory (VTST), its recent theoretical development, and some modern applications.

Transition-State Theory, Dynamics, and Narrow Time Scale Separation in the Rate-Promoting Vibrations Model of Enzyme Catalysis

The power of transition-state theory (TST) for understanding enzymes is evidenced by its recent use in the design and synthesis of highly active de novo enzymes. However, dynamics can influence reaction kinetics, and some studies of rate-promoting vibrations even claim that dynamical theories instead of TST are needed to understand enzymatic reaction mechanisms. For the rate-promoting vibration (RPV) model of enzyme catalysis [Antoniou et al., J. Chem. Phys. 2004, 121, 6442], a reactive flux correlation function analysis shows that dynamical effects do slow the kinetics. However, the RPV model also shows extremely long-lived correlations because the RPV and the bath are not directly coupled. Additionally, earlier studies of the RPV model show a narrow time scale separation due to a small 5kT barrier. Thus earlier findings based on the RPV model may have little bearing on the properties of real enzymes. The intrinsic reaction coordinate (IRC) reveals that the RPV is an important component of the reaction coordinate at early and late stages of the pathway, but the RPV is not an important component of the reaction coordinate direction at the transition state. The unstable eigenmode from harmonic TST (which coincides with the IRC at the saddle point) gives a larger transmission coefficient than the coordinate used in the correlation functions of Antoniou et al. Thus while TST cannot predict the transmission coefficient, the RPV model suggests that TST can provide mechanistic insights on elementary steps in enzyme catalysis. Finally, we propose a method for using the transition-state ensemble as predicted from harmonic TST to distinguish promoting vibrations from other more mundane bath variables.

Transition state theory for enzyme kinetics

This article is an essay that discusses the concepts underlying the application of modern transition state theory to reactions in enzymes. Issues covered include the potential of mean force, the quantization of vibrations, the free energy of activation, and transmission coefficients to account for nonequilibrium effect, recrossing, and tunneling.

Determination of Spin Inversion Probability, H-Tunneling Correction, and Regioselectivity in the Two-State Reactivity of Nonheme Iron(IV)-Oxo Complexes

We show by experiments that nonheme Fe(IV)O species react with cyclohexene to yield selective hydrogen atom transfer (HAT) reactions with virtually no C═C epoxidation. Straightforward DFT calculations reveal, however, that C═C epoxidation on the S = 2 state possesses a low-energy barrier and should contribute substantially to the oxidation of cyclohexene by the nonheme Fe(IV)O species. By modeling the selectivity of this two-site reactivity, we show that an interplay of tunneling and spin inversion probability (SIP) reverses the apparent barriers and prefers exclusive S = 1 HAT over mixed HAT and C═C epoxidation on S = 2. The model enables us to derive a SIP value by combining experimental and theoretical results.

The entropic contributions in vitamin B12 enzymes still reflect the electrostatic paradigm

The catalytic power of enzymes containing coenzyme B12 has been, in some respects, the "last bastion" for the strain hypothesis. Our previous study of this system established by a careful sampling that the major part of the catalytic effect is due to the electrostatic interaction between the ribose of the ado group and the protein and that the strain contribution is very small. This finding has not been sufficiently appreciated due to misunderstandings of the power of the empirical valence bond (EVB) calculations and the need of sufficient sampling. Furthermore, some interesting new experiments point toward entropic effects as the source of the catalytic power, casting doubt on the validity of the electrostatic idea, at least, in the case of B12 enzymes. Here, we focus on the observation of the entropic effects and on analyzing their origin. We clarify that our EVB approach evaluates free energies rather than enthalpies and demonstrate by using the restraint release (RR) approach that the observed entropic contribution to the activation barrier is of electrostatic origin. Our study illustrates the power of the RR approach by evaluating the entropic contributions to catalysis and provides further support to our paradigm for the origin of the catalytic power of B12 enzymes. Overall, our study provides major support to our electrostatic preorganization idea and also highlights the basic requirements from ab initio quantum mechanics/molecular mechanics calculations of activation free energies of enzymatic reactions.

The importance of ensemble averaging in enzyme kinetics

The active site of an enzyme is surrounded by a fluctuating environment of protein and solvent conformational states, and a realistic calculation of chemical reaction rates and kinetic isotope effects of enzyme-catalyzed reactions must take account of this environmental diversity. Ensemble-averaged variational transition state theory with multidimensional tunneling (EA-VTST/MT) was developed as a way to carry out such calculations. This theory incorporates ensemble averaging, quantized vibrational energies, energy, tunneling, and recrossing of transition state dividing surfaces in a systematic way. It has been applied successfully to a number of hydrogen-, proton-, and hydride-transfer reactions. The theory also exposes the set of effects that should be considered in reliable rate constants calculations.

We first review the basic theory and the steps in the calculation. A key role is played by the generalized free energy of activation profile, which is obtained by quantizing the classical potential of mean force as a function of a reaction coordinate because the one-way flux through the transition state dividing surface can be written in terms of the generalized free energy of activation. A recrossing transmission coefficient accounts for the difference between the one-way flux through the chosen transition state dividing surface and the net flux, and a tunneling transmission coefficient converts classical motion along the reaction coordinate to quantum mechanical motion. The tunneling calculation is multidimensional, accounting for the change in vibrational frequencies along the tunneling path and shortening of the tunneling path with respect to the minimum energy path (MEP), as promoted by reaction-path curvature. The generalized free energy of activation and the transmission coefficients both involve averaging over an ensemble of reaction paths and conformations, and this includes the coupling of protein motions to the rearrangement of chemical bonds in a statistical mechanically correct way. The standard deviations of the transmissions coefficients provide information on the diversity of the distribution of reaction paths, barriers, and protein conformations along the members of an ensemble of reaction paths passing through the transition state.

We first illustrate the theory by discussing the application to both wild-type and mutant Escherichia coli dihydrofolate reductase and hyperthermophilic Thermotoga maritima dihydrofolate reductase (DHFR); DHFR is of special interest because the protein conformational changes have been widely studied. Then we present shorter discussions of several other applications of EA-VTST/MT to transfer of protons, hydrogen atoms, and hydride ions and their deuterated analogs. Systems discussed include hydride transfer in alcohol dehydrogenase, xylose isomerase, and thymidylate synthase, proton transfer in methylamine dehydrogenase, hydrogen atom transfer in methylmalonyl-CoA mutase, and nucleophilic substitution in haloalkane dehalogenase and two-dimensional potentials of mean force for potentially coupled proton and hydride transfer in the β-oxidation of butyryl-coenzyme A catalyzed by short-chain acyl-CoA dehydrogenase and in the pyruvate to lactate transformation catalyzed by lactate dehydrogenase.

Glutamate 338 is an electrostatic facilitator of C-Co bond breakage in a dynamic/electrostatic model of catalysis by ornithine aminomutase

How cobalamin-dependent enzymes promote C–Co homolysis to initiate radical catalysis has been debated extensively. For the pyridoxal 5′-phosphate and cobalamin-dependent enzymes lysine 5,6-aminomutase and ornithine 4,5-aminomutase (OAM), large-scale re-orientation of the cobalamin-binding domain linked to C–Co bond breakage has been proposed. In these models, substrate binding triggers dynamic sampling of the B₁₂-binding Rossmann domain to achieve a catalytically competent ‘closed’ conformational state. In ‘closed’ conformations of OAM, Glu338 is thought to facilitate C–Co bond breakage by close association with the cobalamin adenosyl group. We investigated this using stopped-flow continuous-wave photolysis, viscosity dependence kinetic measurements, and electron paramagnetic resonance spectroscopy of a series of Glu338 variants. We found that substrate-induced C–Co bond homolysis is compromised in Glu388 variant forms of OAM, although photolysis of the C–Co bond is not affected by the identity of residue 338. Electrostatic interactions of Glu338 with the 5′-deoxyadenosyl group of B₁₂ potentiate C–Co bond homolysis in ‘closed’ conformations only; these conformations are unlocked by substrate binding. Our studies extend earlier models that identified a requirement for large-scale motion of the cobalamin domain. Our findings indicate that large-scale motion is required to pre-organize the active site by enabling transient formation of ‘closed’ conformations of OAM. In ‘closed’ conformations, Glu338 interacts with the 5′-deoxyadenosyl group of cobalamin. This interaction is required to potentiate C–Co homolysis, and is a crucial component of the approximately 10¹² rate enhancement achieved by cobalamin-dependent enzymes for C–Co bond homolysis.

How does tunneling contribute to counterintuitive H-abstraction reactivity of nonheme Fe(IV)O oxidants with alkanes?

This article addresses the intriguing hydrogen-abstraction (H-abstraction) and oxygen-transfer (O-transfer) reactivity of a series of nonheme [Fe(IV)(O)(TMC)(Lax)](z+) complexes, with a tetramethyl cyclam ligand and a variable axial ligand (Lax), toward three substrates: 1,4-cyclohexadiene, 9,10-dihydroanthracene, and triphenyl phosphine. Experimentally, O-transfer-reactivity follows the relative electrophilicity of the complexes, whereas the corresponding H-abstraction-reactivity generally increases as the axial ligand becomes a better electron donor, hence exhibiting an antielectrophilic trend. Our theoretical results show that the antielectrophilic trend in H-abstraction is affected by tunneling contributions. Room-temperature tunneling increases with increase of the electron donation power of the axial-ligand, and this reverses the natural electrophilic trend, as revealed through calculations without tunneling, and leads to the observed antielectrophilic trend. By contrast, O-transfer-reactivity, not being subject to tunneling, retains an electrophilic-dependent reactivity trend, as revealed experimentally and computationally. Tunneling-corrected kinetic-isotope effect (KIE) calculations matched the experimental KIE values only if all of the H-abstraction reactions proceeded on the quintet state (S = 2) surface. As such, the present results corroborate the initially predicted two-state reactivity (TSR) scenario for these reactions. The increase of tunneling with the electron-releasing power of the axial ligand, and the reversal of the "natural" reactivity pattern, support the "tunneling control" hypothesis (Schreiner et al., ref 19). Should these predictions be corroborated, the entire field of C-H bond activation in bioinorganic chemistry would lay open to reinvestigation.

A mechanochemical switch to control radical intermediates

B₁₂-dependent enzymes employ radical species with exceptional prowess to catalyze some of the most chemically challenging, thermodynamically unfavorable reactions. However, dealing with highly reactive intermediates is an extremely demanding task, requiring sophisticated control strategies to prevent unwanted side reactions. Using hybrid quantum mechanical/molecular mechanical simulations, we follow the full catalytic cycle of an AdoB₁₂-dependent enzyme and present the details of a mechanism that utilizes a highly effective mechanochemical switch. When the switch is "off", the 5'-deoxyadenosyl radical moiety is stabilized by releasing the internal strain of an enzyme-imposed conformation. Turning the switch "on," the enzyme environment becomes the driving force to impose a distinct conformation of the 5'-deoxyadenosyl radical to avoid deleterious radical transfer. This mechanochemical switch illustrates the elaborate way in which enzymes attain selectivity of extremely chemically challenging reactions.

Role of active site residues in promoting cobalt-carbon bond homolysis in adenosylcobalamin-dependent mutases revealed through experiment and computation

Adenosylcobalamin (AdoCbl) serves as a source of reactive free radicals that are generated by homolytic scission of the coenzyme's cobalt-carbon bond. AdoCbl-dependent enzymes accelerate AdoCbl homolysis by ∼10(12)-fold, but the mechanism by which this is accomplished remains unclear. We have combined experimental and computational approaches to gain molecular-level insight into this process for glutamate mutase. Two residues, glutamate 330 and lysine 326, form hydrogen bonds with the adenosyl group of the coenzyme. A series of mutations that impair the enzyme's ability to catalyze coenzyme homolysis and tritium exchange with the substrate by 2-4 orders of magnitude were introduced at these positions. These mutations, together with the wild-type enzyme, were also characterized in silico by molecular dynamics simulations of the enzyme-AdoCbl-substrate complex with AdoCbl modeled in the associated (Co-C bond formed) or dissociated [adenosyl radical with cob(II)alamin] state. The simulations reveal that the number of hydrogen bonds between the adenosyl group and the protein side chains increases in the homolytically dissociated state, with respect to the associated state, for both the wild-type and mutant enzymes. The mutations also cause a progressive increase in the mean distance between the 5'-carbon of the adenosyl radical and the abstractable hydrogen of the substrate. Interestingly, the distance between the 5'-carbon and substrate hydrogen, determined computationally, was found to inversely correlate with the log k for tritium exchange (r = 0.93) determined experimentally. Taken together, these results point to a dual role for these residues: they both stabilize the homolytic state through electrostatic interactions between the protein and the dissociated coenzyme and correctly position the adenosyl radical to facilitate the abstraction of hydrogen from the substrate.

Army ants tunneling for classical simulations

We present an algorithm, called army ants tunneling, for adding tunneling to classical trajectories by means of quantal rare event sampling.

Hydrogen transfer reactions in viscous media — Potential and free energy surfaces in solvent–solute coordinates and their kinetic implications

Two-dimensional potential energy and free energy surfaces are obtained using quantum mechanical and molecular dynamics calculations for four hydrogen transfer reactions in n-hexane solvent: the methyl–methane, n-propyl–n-propane, n-pentyl–n-pentane, and t-butyl–isobutane systems. The resultant surfaces have similar landscapes despite the fact the equilibrated solvent cavities for these systems are notably different in size and shape. The kinetic implications of these landscapes are discussed. The Arrhenius and tunneling kinetics of hydrogen transfer in nonpolar hydrocarbon solute–solvent systems are not expected to show any significant viscosity dependence.

Adenosylcobalamin enzymes: theory and experiment begin to converge

Adenosylcobalamin (coenzyme B(12)) serves as the cofactor for a group of enzymes that catalyze unusual rearrangement or elimination reactions. The role of the cofactor as the initiator of reactive free radicals needed for these reactions is well established. Less clear is how these enzymes activate the coenzyme towards homolysis and control the radicals once generated. The availability of high resolution X-ray structures combined with detailed kinetic and spectroscopic analyses have allowed several adenosylcobalamin enzymes to be computationally modeled in some detail. Computer simulations have generally obtained good agreement with experimental data and provided valuable insight into the mechanisms of these unusual reactions. Importantly, atomistic modeling of the enzymes has allowed the role of specific interactions between protein, substrate and coenzyme to be explored, leading to mechanistic predictions that can now be tested experimentally. This article is part of a Special Issue entitled: Radical SAM enzymes and Radical Enzymology.

Taking Ockham's razor to enzyme dynamics and catalysis

The role of protein dynamics in enzyme catalysis is a matter of intense current debate. Enzyme-catalysed reactions that involve significant quantum tunnelling can give rise to experimental kinetic isotope effects with complex temperature dependences, and it has been suggested that standard statistical rate theories, such as transition-state theory, are inadequate for their explanation. Here we introduce aspects of transition-state theory relevant to the study of enzyme reactivity, taking cues from chemical kinetics and dynamics studies of small molecules in the gas phase and in solution--where breakdowns of statistical theories have received significant attention and their origins are relatively better understood. We discuss recent theoretical approaches to understanding enzyme activity and then show how experimental observations for a number of enzymes may be reproduced using a transition-state-theory framework with physically reasonable parameters. Essential to this simple model is the inclusion of multiple conformations with different reactivity.

Two-dimensional infrared spectroscopy of azido-nicotinamide adenine dinucleotide in water

Mid-IR active analogs of enzyme cofactors have the potential to be important spectroscopic reporters of enzyme active site dynamics. Azido-nicotinamide adenine dinucleotide (NAD(+)), which has been recently synthesized in our laboratory, is a mid-IR active analog of NAD(+), a ubiquitous redox cofactor in biology. In this study, we measure the frequency-frequency time correlation function for the antisymmetric stretching vibration of the azido group of azido-NAD(+) in water. Our results are consistent with previous studies of pseudohalides in water. We conclude that azido-NAD(+) is sensitive to local environmental fluctuations, which, in water, are dominated by hydrogen-bond dynamics of the water molecules around the probe. Our results demonstrate the potential of azido-NAD(+) as a vibrational probe and illustrate the potential of substituted NAD(+)-analogs as reporters of local structural dynamics that could be used for studies of protein dynamics in NAD-dependent enzymes.

The fragmentation-recombination mechanism of the enzyme glutamate mutase studied by QM/MM simulations

The radical mechanism of the conversion of glutamate to methylaspartate catalyzed by glutamate mutase is studied with quantum mechanical/molecular mechanical (QM/MM) simulations based on density functional theory (DFT/MM). The hydrogen transfer between the substrate and the cofactor is found to be rate limiting with a barrier of 101.1 kJ mol(-1). A careful comparison to the uncatalyzed reaction in water is performed. The protein influences the reaction predominantly electrostatically and to a lesser degree sterically. Our calculations shed light on the atomistic details of the reaction mechanism. The well-known arginine claw and Glu 171 ( Clostridium cochlearium notation) are found to have the strongest influence on the reaction. However, a catalytic role of Glu 214, Lys 322, Gln 147, Glu 330, Lys 326, and Met 294 is found as well. The arginine claw keeps the intermediates in place and is probably responsible for the enantioselectivity. Glu 171 temporarily accepts a proton from the glutamyl radical intermediate and donates it back at the end of the reaction. We relate our results to experimental data when available. Our simulations lead to further understanding of how glutamate mutase catalyzes the carbon skeleton rearrangement of glutamate.

Direct Dynamics Implementation of the Least-Action Tunneling Transmission Coefficient. Application to the CH4/CD3H/CD4 + CF3 Abstraction Reactions

We present two new direct dynamics algorithms for calculating transmission coefficients of polyatomic chemical reactions by the multidimensional least-action tunneling approximation. The new algorithms are called the interpolated least-action tunneling method based on one-dimensional interpolation (ILAT1D) and the double interpolated least-action tunneling (DILAT) method. The DILAT algorithm, which uses a one-dimensional spline under tension to interpolate both of the effective potentials along the nonadiabatic portions of tunneling paths and the imaginary action integrals as functions of tunneling energies, was designed for the calculation of multidimensional LAT transmission coefficients for very large polyatomic systems. The performance of this algorithm has been tested for the CH4/CD3H/CD4 + CF3 hydrogen abstraction reactions with encouraging results, i.e., when the fitting is performed using 13 points, the algorithm is about 30 times faster than the full calculation with deviations that are smaller than 5%. This makes direct dynamics least-action tunneling calculations practical for larger systems, higher levels of electron correlation, and/or larger basis sets.

Importance of the lactate dehydrogenase quaternary structure in theoretical calculations

Using the example of lactate dehydrogenase, we show that enzyme quaternary structure has an important influence on the structure of the active site and that models that comprise all amino acids in the vicinity of an active site, but are missing this structural information, can lead to incorrect results. We also show that binding isotope effects are very sensitive to the geometric parameters, and thus one should be very cautious when interpreting results obtained with models that are too coarse. In terms of the type of hydrogen bonds, our results indicate that binding isotope effects are pronounced only when a hydrogen bond exhibits some covalent character.

At the dawn of the 21st century: Is dynamics the missing link for understanding enzyme catalysis?

Enzymes play a key role in almost all biological processes, accelerating a variety of metabolic reactions as well as controlling energy transduction, the transcription, and translation of genetic information, and signaling. They possess the remarkable capacity to accelerate reactions by many orders of magnitude compared to their uncatalyzed counterparts, making feasible crucial processes that would otherwise not occur on biologically relevant timescales. Thus, there is broad interest in understanding the catalytic power of enzymes on a molecular level. Several proposals have been put forward to try to explain this phenomenon, and one that has rapidly gained momentum in recent years is the idea that enzyme dynamics somehow contributes to catalysis. This review examines the dynamical proposal in a critical way, considering basically all reasonable definitions, including (but not limited to) such proposed effects as "coupling between conformational and chemical motions," "landscape searches" and "entropy funnels." It is shown that none of these proposed effects have been experimentally demonstrated to contribute to catalysis, nor are they supported by consistent theoretical studies. On the other hand, it is clarified that careful simulation studies have excluded most (if not all) dynamical proposals. This review places significant emphasis on clarifying the role of logical definitions of different catalytic proposals, and on the need for a clear formulation in terms of the assumed potential surface and reaction coordinate. Finally, it is pointed out that electrostatic preorganization actually accounts for the observed catalytic effects of enzymes, through the corresponding changes in the activation free energies.

Hydrogen tunneling in adenosylcobalamin-dependent glutamate mutase: evidence from intrinsic kinetic isotope effects measured by intramolecular competition

Hydrogen atom transfer reactions between the substrate and coenzyme are key mechanistic features of all adenosylcobalamin-dependent enzymes. For one of these enzymes, glutamate mutase, we have investigated whether hydrogen tunneling makes a significant contribution to the mechanism by examining the temperature dependence of the deuterium kinetic isotope effect associated with the transfer of a hydrogen atom from methylaspartate to the coenzyme. To do this, we designed a novel intramolecular competition experiment that allowed us to measure the intrinsic kinetic isotope effect, even though hydrogen transfer may not be rate-determining. From the Arrhenius plot of the kinetic isotope effect, the ratio of the pre-exponential factors (A(H)/A(D)) was 0.17 +/- 0.04 and the isotope effect on the activation energy [DeltaE(a(D-H))] was 1.94 +/- 0.13 kcal/mol. The results imply that a significant degree of hydrogen tunneling occurs in glutamate mutase, even though the intrinsic kinetic isotope effects are well within the semiclassical limit and are much smaller than those measured for other AdoCbl enzymes and model reactions for which hydrogen tunneling has been implicated.

Adenosyl radical: reagent and catalyst in enzyme reactions

Adenosine is undoubtedly an ancient biological molecule that is a component of many enzyme cofactors: ATP, FADH, NAD(P)H, and coenzyme A, to name but a few, and, of course, of RNA. Here we present an overview of the role of adenosine in its most reactive form: as an organic radical formed either by homolytic cleavage of adenosylcobalamin (coenzyme B(12), AdoCbl) or by single-electron reduction of S-adenosylmethionine (AdoMet) complexed to an iron-sulfur cluster. Although many of the enzymes we discuss are newly discovered, adenosine's role as a radical cofactor most likely arose very early in evolution, before the advent of photosynthesis and the production of molecular oxygen, which rapidly inactivates many radical enzymes. AdoCbl-dependent enzymes appear to be confined to a rather narrow repertoire of rearrangement reactions involving 1,2-hydrogen atom migrations; nevertheless, mechanistic insights gained from studying these enzymes have proved extremely valuable in understanding how enzymes generate and control highly reactive free radical intermediates. In contrast, there has been a recent explosion in the number of radical-AdoMet enzymes discovered that catalyze a remarkably wide range of chemically challenging reactions; here there is much still to learn about their mechanisms. Although all the radical-AdoMet enzymes so far characterized come from anaerobically growing microbes and are very oxygen sensitive, there is tantalizing evidence that some of these enzymes might be active in aerobic organisms including humans.

On the importance of ribose orientation in the substrate activation of the coenzyme B12-dependent mutases

The degree to which the corrin ring portion of coenzyme B(12) can facilitate the H-atom-abstraction step in the glutamate mutase (GM)-catalyzed reaction of (S)-glutamate has been investigated with density functional theory. The crystal structure of GM identifies two possible orientations of the ribose portion of coenzyme B(12). In one orientation (A), the OH groups of the ribose extend away from the corrin ring, whereas in the other orientation (B) the OH groups, especially that involving O3', are instead directed towards the corrin ring. Our calculations identify a sizable stabilization amounting to about 30 kJ mol(-1) in the transition structure (TS) complex corresponding to orientation B (TS(B)CorIm). In the TS complex where the ribose instead is positioned in orientation A, no such effect is manifested. The observed stabilization in TS(B)CorIm appears to be the result of favorable interactions involving O3' and the corrin ring, including a C-HO hydrogen bond. We find that the degree of stabilization is not particularly sensitive to the Co-C distance. Our calculations show that any potential stabilization afforded to the H-atom-abstraction step by coenzyme B(12) is sensitive to the orientation of the ribose moiety.

DFT and ONIOM(DFT:MM) studies on Co-C bond cleavage and hydrogen transfer in B12-dependent methylmalonyl-CoA mutase. Stepwise or concerted mechanism?

The considerable protein effect on the homolytic Co-C bond cleavage to form the 5'-deoxyadenosyl (Ado) radical and cob(II)alamin and the subsequent hydrogen transfer from the methylmalonyl-CoA substrate to the Ado radical in the methylmalonyl-CoA mutase (MMCM) have been extensively studied by DFT and ONIOM(DFT/MM) methods. Several quantum models have been used to systematically study the protein effect. The calculations have shown that the Co-C bond dissociation energy is very much reduced in the protein, compared to that in the gas phase. The large protein effect can be decomposed into the cage effect, the effect of coenzyme geometrical distortion, and the protein MM effect. The largest contributor is the MM effect, which mainly consists of the interaction of the QM part of the coenzyme with the MM part of the coenzyme and the surrounding residues. In particular, Glu370 plays an important role in the Co-C bond cleavage process. These effects tremendously enhance the stability of the Co-C bond cleavage state in the protein. The initial Co-C bond cleavage and the subsequent hydrogen transfer were found to occur in a stepwise manner in the protein, although the concerted pathway for the Co-C bond cleavage coupled with the hydrogen transfer is more favored in the gas phase. The assumed concerted transition state in the protein has more deformation of the coenzyme and the substrate and has less interaction with the protein than the stepwise route. Key factors and residues in promoting the enzymatic reaction rate have been discussed in detail.

A possible mechanism for evading temperature quantum decoherence in living matter by feshbach resonance

A new possible scenario for the origin of the molecular collective behaviour associated with the emergence of living matter is presented. We propose that the transition from a non-living to a living cell could be mapped to a quantum transition to a coherent entanglement of condensates, like in a multigap BCS superconductor. Here the decoherence-evading qualities at high temperature are based on the Feshbach resonance that has been recently proposed as the driving mechanism for high T_c superconductors. Finally we discuss how the proximity to a particular critical point is relevant to the emergence of coherence in the living cell.

Insights into the mechanisms of adenosylcobalamin (coenzyme B12)-dependent enzymes from rapid chemical quench experiments

Glutamate mutase is one of a group of adenosylcobalamin-dependent enzymes that use free radicals to catalyse unusual and chemically difficult rearrangements involving 1,2-migrations of hydrogen atoms. A key mechanistic feature of these enzymes is the transfer of the migrating hydrogen atom between substrate, coenzyme and product. The present review summarizes recent experiments from my laboratory that have used rapid chemical quench techniques to identify intermediates in the reaction and probe the mechanism of hydrogen transfer through a variety of pre-steady-state kinetic isotope effect measurements.