Báo cáo Y học: Environmentally coupled hydrogen tunneling Linking catalysis to dynamics

Eur. J. Biochem. 269, 3113–3121 (2002) Ó FEBS 2002 doi:10.1046/j.1432-1033.2002.03022.x MINIREVIEW Environmentally coupled hydrogen tunneling Linking catalysis to dynamics Michael J. Knapp1 and Judith P. Klinman1,2 1Department of Chemistry and 2Department of Molecular and Cell Biology, University of California, Berkeley, USA Many biological C-H activation reactions exhibit nonclas-sical kinetic isotope effects (KIEs). These nonclassical KIEs are too large (kH/kD > 7) and/or exhibit unusual tempera-ture 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 tun-neling 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 quan-tumviewofhydrogentransfernecessarilyadynamicviewof INTRODUCTION Quantum effects have long been appreciated in biological electrontransfer (ET)reactions, due to thelargeuncertainty inpositionforthee–.ThequantumnatureofEThasrequired new reaction models that go beyond transition-state theory. Marcus recognized the contribution of heavy-atom coordi- natestotherateofETthroughanenvironmentalenergyterm ðkET / eDGz=RT Þ, where DGà is the free energy barrier to reaction,Risthegasconstant,andTisabsolutetemperature [1]. Importantly, the reaction coordinate according to Marcus theory is, to a large extent, determined by the heavy atom coordinates and not by the e– coordinate. This remarkableinsightisinstarkcontrasttotypicalassumptions Correspondence to J. P. Klinman, Department of Chemistry, University of California, Berkeley, CA 94720, USA. Fax: + 1 510 643 6232, Tel.: + 1 510 642 2668, E-mail: klinman@socrates.berkeley.edu Abbreviations: ET, electron transfer; KIE, kinetic isotope effect; Dkcat, kinetic isotopeeffect on kcat; 13-(S)-HPOD, 13-(S)-hydroperoxy-9,11-(Z,E)-octadecadienoic acid; LA, linoleic acid, 9,12-(Z,Z)-octadecadi-enoic acid; TST, transition-state theory; TS, transition-state; (WT)-SLO, (wild-type) soybean lipoxygenase-1; ht-ADH, thermo-philic alcohol dehydrogenase; VT-KIE, variable temperature kinetic isotope effect. Definition: The term semiclassical refers to a model in which kinetic isotope effects arise from differences in the zero-point energies of the C-H and C-D stretches. (Received 12 March 2002, revised 31 May 2002, accepted 6 June 2002) 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 tem-peraturedependenceoftheKIEwithinthismodel,providing insightintotheimportanceofthismotioninmodulatingthe reaction coordinate. The potential use of variable tempera-ture KIEs as a direct probe of coupling between environ-mental dynamics and the reaction coordinate is described. Theevolutionfromapplicationofatunnelingcorrectiontoa full tunneling model in enzymatic H transfer reactions is discussed in the context of a thermophilic alcohol dehy-drogenase and soybean lipoxygenase-1. Keywords: hydrogen tunneling; kinetic isotope effects; lip-oxygenase; protein dynamics; reaction coordinate. that the reaction coordinate for heavier particles is domin-ated by the transferring group. Hydrogen transfer (H+, H–, or H•) is another well known reaction in which appreciable quantum-mechanical behavior is evident [2–10]. We are at a crucial juncture in our understanding of hydrogen transfer, as theoretical models accounting for its nonclassical nature are being developed [11–15]. A key feature of these theor-etical models is the proposed involvement of environmental dynamics along the reaction coordinate. Can experimental-ists rise to the challenge that is presented by theorists, and find evidence for dynamics that couple to catalysis? On the basis of general physical principles, it should not be surprising that a hydrogen transfer exhibits nonclassical behavior. Hydrogen is a light particle, with a large uncertainty in its position. A measure of this uncertainty is the deBroglie wavelength, k ¼ h/ 2mE, in which h is Planck’s constant, m is the mass of the particle, and E is its energy. Assuming an energy of 20 kJÆmol)1 ( 5 kcalÆ mol)1) the deBroglie wavelength is calculated to be 0.63 A and 0.45 A for protium (H, or 1H) and deuterium (D, or 2H),respectively.Ashydrogenistypically transferredovera similar distance (< 1 A), this positional uncertainty is significant, and implicates considerable nonclassical proper-ties for hydrogen transfers. Despitetheunderlying quantum nature of hydrogen transfer, such reactions frequently mimic classical reactions (as by exhibiting a positive temperature dependence); for this reason, hydrogen tunnel-inghastypicallybeentreatedasaperturbationoftransition-state theory (TST) [16,17]. While TST remains the common language of chemical reactions, increasing numbers of workers are coming to 3114 M. J. Knapp and J. P. Klinman (Eur. J. Biochem. 269) Ó FEBS 2002 appreciate [18] that such a model is over-simplified, as data accumulate regarding the importance of quantum effects [19,20] and dynamics [21–23] in enzyme catalysis. Bell treated small deviations from classical behavior by correct-ing the TST rates of hydrogen transfer for a finite tunneling probability. In contrast to this are dissipative tunneling models, in which hydrogen transfer is treated fully quan-tum-mechanically, and interactions with the environment can make the reaction ÔappearÕ classical. We will discuss the progression in our thinking about hydrogen transfer, from the tunnel corrections initially applied to hydride (H–) transfers, to the full-tunneling models applicable to hydro-gen atom (H•) transfers. SEMICLASSICAL KINETIC ISOTOPE EFFECTS AND TUNNELING CORRECTIONS Theories of enzyme catalysis have focussed on energetic effects [24], such as the oft-cited concept of transition-state stabilization [18]. Such explanations are aesthetically pleas- ing,inthatactivatedcomplextheoryformulatestherateofa reaction as ðkTST ¼ AeDGz=RT Þ, in which A is a pre- exponential term, and DG is the energetic barrier to reaction. It is natural to focus attention on the exponential term, as a relatively small change in DGà leads to a large change in kTST. Reducing DGà can be achieved by either stabilizing the transition-state, or by ground-state destabil-ization; both lead to a similar reduction in DGà, and significant alterations in kTST. Kinetic isotope effects (KIEs) are mainstays for probing chemical mechanisms, as they provide information on the reaction coordinates. Primary (1°) KIEs are due to the hydrogen that is transferred during a reaction. The semi-classical KIE model, also called the bond-stretch model (Fig. 1A) proposes that 1° KIEs arise from differences in the zero-point energy upon isotopic substitution, and formulates the rate of reaction as kH ¼ AH exp {–(DG ) ½hmH)/RT}, where mH is the vibrational fre-quency of the transferred hydrogen and h is Planck’s constant [17]. When comparing protium to deuterium, the resultant variable temperature KIE is kH/kD ¼ (AH/AD) exp{(½hmH ) ½hmD)/RT}. This neglects compensatory motions in the transition state that could act to reduce the size of the KIE [25]. The simple bond-stretch formalism predicts an appreciable KIE at room temperature ( 7 at 300 K), which vanishes at infinite temperature, as AH/ AD 1 in this model. All further references to KIEs within this review will be to 1° KIEs, unless noted otherwise. Earlier theoretical treatments for hydrogen tunneling were focussed on the Bell model [16], which was developed toexplainsomeofthepeculiarbehavioroforganicreactions in solution. Tunneling occurs just below the classical transition-state in the Bell model, resulting in a relatively small correction to the overall reaction rate and isotope effect (Fig. 1B); depending on the extent of H or D tunneling, different KIE patterns are predicted [26,27]. This model is characterized by certain deviations of KIEs from those calculated in the semiclassical model: inflated kinetic isotope effects (H/D KIEs > 7), and an inverse isotope effect on the Arrhenius prefactor ratios (AH/AD < 1) as measured by variable-temperature KIEs (VT-KIEs) [26]. Additionally, the exponent relating the three hydrogen Fig. 1. Hydrogen transfer reaction coordinate diagram, illustrating the semiclassical (bond-stretch) model for kinetic isotope effects (A) and the tunneling correction to the semiclassical model (B). (A) DGà is the free energy barrier to hydrogen transfer, ½hmH and ½hmD denote the zero-point energy for the C–H and C–D stretches, respectively. (B) Hydrogen transfer reaction coordinate diagram illustrating the tun-neling correction to the semiclassical model. H tunnels through the barrier at a lower energy than does D. isotopes (H/T vs. D/T) has a characteristic value in the semiclassical model [kH/kT ¼ (kD/kT)3.3]; in mixed-label KIE measurements, positive deviations from this value (so-called Swain–Schaad deviations) have been presented as evidence for tunneling within the Bell formalism [27]. In 1989, our group reported an elevated Swain–Schaad exponent [kH/kT > (kD/kT)3.3] for the secondary (2°) KIE in the alcohol oxidation catalyzed by yeast alcohol dehy-drogenase, demonstrating hydride (H–) tunneling at room temperature [2] (these a-2° KIEs are due to the nontrans-ferred hydrogen of the alcohol). This research article was rapidly followed by several other examples of hydrogen tunneling, demonstrated by either Swain–Schaad deviations or by Arrhenius prefactor ratios deviating from semiclas-sical limits (AH/AD 1). Swain–Schaad deviations for the 2° KIEs in mixed-label experiments were used to demon-strate tunneling in horse liver alcohol dehydrogenase [28]. VT-KIEs were used to demonstrate tunneling through 1° AH/AD ratioswhichdeviatedfromunityintheproton(H+) transfer catalyzed by bovine serum amine oxidase [5], and the H• (or H+) transfer in monoamine oxidase-B [29]. The observed KIEs were all consistent with a tunnel-correction to a semiclassical hydrogen transfer. Ó FEBS 2002 Hydrogen tunneling and protein dynamics (Eur. J. Biochem. 269) 3115 BREAKING THE TUNNEL-CORRECTION: THERMOPHILIC ALCOHOL DEHYDROGENASE AND SOYBEAN LIPOXYGENASE-1 Much of the early evidence for enzymatic hydrogen tunneling could be explained within a tunnel-correction model, as for the small-molecule reactions. This worked very well for the moderate deviations of KIEs from semiclassical predictions. Additional KIEs have been reportedby thislab [3,6,7], andby Scruttonand coworkers [8,10], that are inconsistent with modest tunneling correc-tions, and provide support for environmentally coupled hydrogen tunneling. In both the thermophilic ADH from Bacillus stearothermophilus (ht-ADH) and soybean lipoxyg-enase (SLO), VT-KIEs revealed inflated Arrhenius prefac-tor ratios ( H/AD 1) and finite activation energies (Eact „ 0) that are incompatible with the Bell model [6,7]. Furthermore, the AH/AD ratios were observed to become inverse upon perturbing the system, with the perturbant being temperature in ht-ADH, and site-specific mutagenesisinSLO.Asdiscussedbelow,awidevariationin AH/AD can, in fact, be explained as arising from alterations in the environmental dynamics that modulate hydrogen tunneling. ThephysiologicaltemperatureofB. stearothermophilusis 60–70 °C, sufficiently high that it was possible for Kohen et al. to collect KIE data over a very wide temperature range (5–65 °C) [7]. ht-ADH exhibited a Swain–Schaad exponent on the 2° KIEs that exceeded 3.3 at all temper-atures, indicating that the reaction catalyzed by ht-ADH involves tunneling by this standard criterion. Furthermore, the exponent increased as a function of temperature, from 5 ( 5°C) to 14 (65 °C), which suggested that tunneling increasedasafunctionoftemperature,contrarytostandard views of temperature effects on tunneling. To further complicate the picture, a convex Arrhenius plot was obtained from the kinetic data, with a break point at 30 °C, below which kcat exhibited an increased activation energy. Below 30 °C, the 1° KIEs exhibit an inverse AH/AD ratio (AH/AD ¼ 1 · 10 ), whereas the KIEs above 30 °C show an AH/AD ratio greater than unity (AH/AD ¼ 2). Sizeableactivationenergies,togetherwithinverseArrhenius prefactor ratios, are predicted within the Bell model when tunneling is significant; however, prefactor ratios greater than unity are not. Accommodating ht-ADH within any model requires that onetreattheenzymeasifitexistsintwophasesseparatedby temperature, each with a different reaction coordinate and extent of tunneling. It is not simple to predict why the signatures of tunneling should be more pronounced at high temperature. However, it was suggested that promotion of hydrogen transfer via environmental oscillations could provide an explanation of the data in ht-ADH [7]. Deuterium exchange experiments indicated greater flexibil-ity of the ht-ADH at 60 °C than at reduced temperature (25 °C), suggesting a correlation between global enzyme flexibility and the extent of tunneling, and lending support to the notion that environmental oscillations may modulate hydrogen transfer [30]. In this view, the promoting vibrations become Ôfrozen-outÕ below 30 °C, such that hydrogen transfer is dominated by a more classical reaction coordinate with a portion of H transfer occurring through- the barrier. Above 30 °C, available protein oscillations contribute to the reaction coordinate, greatly increasing the role of tunneling in the hydrogen transfer. Thus, the experimental data for ht-ADH suggested a link between enzyme dynamics and hydrogen transfer, even within the context of a tunnel-correction model for hydride transfer. Several notable examples of hydrogen atom transfer exhibit KIEs so large that they cannot be explained within anytunneling-correctionmodel[3,31–33].TheH/DKIEfor the H• transfer of WT-SLO is greater than 80 at room temperature, and the activation energy on H• transfer is remarkably small (Eact ¼ 2.1 kcalÆmol)1) [9,34–36]. When this result was reported, it signaled a new era in hydrogen transfer chemistry, as itwas so deviantas to make tunneling corrections of dubious relevance. Explicit tunneling effects are required to accommodate the kinetics of SLO, and may be equally importantin many other hydrogen atom transfer reactions. Many H• transfer reactions are characterized by very large inherent chemical barriers, such that movement through, rather than over, the barrier may dominate the reaction pathway. SLO catalyzes the production of fatty acid hydroper-oxides at 1,4-pentadienyl positions, and the product 13-(S)-hydroperoxy-9,11-(Z,E)-octadecadienoic acid [13-(S)-HPOD] is formed from the physiological substrate linoleic acid (LA) (Scheme 1). This reaction proceeds by an initial, rate-limiting abstraction ofthe pro-Shydrogen from C11 of LA by the Fe3+-OH cofactor, forming a substrate-derived radical intermediate and Fe2+-OH2 [37]. Molecular oxygen rapidly reacts with this radical, eventually forming 13-(S)-HPOD and regenerating resting enzyme. Much of the work substantiating hydrogen tunneling in this reaction has relied on steady-state kinetics, in which the isotope effect on kcat (Dkcat) is determined. The kinetic isolation of the chemical step, together with the magnitude of the KIE, was corroborated by viscosity effects, solvent isotope effects, and single-turnover studies [4,34]. Several otherinvestigationshaveconfirmedthefindingthattheKIE on the chemical step of SLO is 80 at room temperature [6,35], including one notable study that excluded magnetic effectsastheoriginofthisKIE[36].Potentialcomplications in assigning Dkcat to a single chemical step, for example due to a branched reaction mechanism, were also ruled out [34]. Scheme 1. 3116 M. J. Knapp and J. P. Klinman (Eur. J. Biochem. 269) Ó FEBS 2002 Table 1. Kinetic parameters for SLO and mutants in pH 9.0 borate buffer. Data were collected between 5 °C and 50 °C. Standard errors from data fitting are in parentheses. WT-SLO Leu546 fi Ala Leu754 fi Ala Ile553 fi Ala a cat (s–1) 297 (12) 4.8 (0.6) 0.31 (0.02) 280 (10) KIEb 81 (5) 93 (9) 112 (11) 93 (4) Eact (kcalÆmol–1) 2.1 (0.2) 4.1 (0.4) 4.1 (0.3) 1.9 (0.2) DEactc (kcalÆmol–1) 0.9 (0.2) 1.9 (0.6) 2.0 (0.5) 4.0 (0.3) AH/AD 18 (5) 4 (4) 3 (3) 0.12 (0.06) a The rate constants (kcat for 1H31-LA) are reported for 30 °C. b KIE ¼ Dkcat, reported for 30 °C. c This is the isotope effect on Eact, DEact ¼ EactD ) EactH. All data indicate that the chemical step (H• abstraction) is fully rate-limiting on kcat, in WT-SLO, and that the steady-state KIE ( kcat) represents an intrinsic value. An Eyring treatment of the variable temperature data for WT-SLO suggests that the barrier to reaction is dominantly entropic, as the enthalpic barrier (DHà ¼ 1.5 kcalÆmol)1) is much less than the entropic barrier (–TDSà ¼ 12.8 kcalÆmol)1). Such an interpretation becomes meaningless whentherateandKIEsareconsideredwithinthecontextof TST. The KIE is only weakly temperature dependent, and when extrapolated to infinite temperature remains very large (AH/AD ¼ 18; Table 1). This would put the isotope effect predominantly on the entropic term, rather than the enthalpic term as is the norm in reactions modeled by the semiclassicaltheoryofKIEs.Itisclearthatthesemiclassical theory fails to account for the data; furthermore, a tunnel-correction cannot simultaneously reproduce the magnitude and temperature dependence of this KIE. The substrate binding pocket of SLO is lined by bulky hydrophobic residues [38], with Leu546, Leu754, and Ile553 closest to the Fe3+-OH site. Knapp et al. singly mutated these residues to alanine and probed their effects on H tunneling by VT-KIE measurements (Table 1) [6]. Whereas WT-SLO exhibits a large Arrhenius prefactor KIE (AH/AD ¼ 18), the two mutations closest to the reacting position, Leu546 fi Ala, Leu754 fi Ala, change the tem-perature-dependence of the KIE (AH/AD ¼ 3) in a manner that suggests a modest alteration in the tunneling coordi-nate. The more distal mutant, Ile553 fi Ala, exhibits a KIE significantlymoretemperaturedependentthaninWT-SLO, leading to an inverse Arrhenius prefactor KIE (AH/AD ¼ 0.2) that implicates a fundamental change in the tunneling coordinate. Despite the alterations in the temperature dependencies, the KIEs at 30 °C remain large (Dkcat > 80) for each mutant, indicating similar tunneling components for all reactions. From the outset it appeared that a tunneling correction wouldbeunabletoaccountforthemagnitudeoftheKIEin SLO (81–100, depending on the mutation). Nor could such an approach account for the elevated Arrhenius prefactor KIE of WT-SLO. Particularly puzzling was the variation in AH/AD ratio observed in SLO as a function of mutation. A previous formalism of tunneling advanced by this lab relied upon the AH/AD ratio to characterize the extent of tunneling within a static environment [4]. The data would be interpreted within this prior formalism to indicate that WT-SLO (AH/AD 1) approximates deep tunneling behavior (H and D tunnel similarly), that Ile553 fi Ala (AH/AD 1) exhibits moderate tunneling (H tunnels more than D), and that Leu546 fi Ala and Leu754 fi Ala (AH/AD 1) either approach normal classical transfer or exhibit transitional behavior between moderate and deep tunneling. This formalism also requires reduced H/D KIEs as the tunneling changes from extreme to moderate; yet the observed KIEs are always greater than 80, and, in fact, increase in the mutants. Furthermore, this formalism predicts that small Eact values would be accompanied by large AH/AD ratios, yet the Ile553 fi Ala mutant has a small Eact value and a small AH/AD ratio. From every perspective, it became clear that a model invoking different extents of through barrier H transfer for WT-SLO and the mutants would be incorrect. The tunneling behavior observed in SLO and its mutants as a function of mutational position (from AH/AD > 1 to AH/AD < 1) mirrors the tunneling behavior of ht-ADH as a function of temperature. What is unique about the SLO case is that the magnitude of the KIE (kH/kD > 80 at 30 °C) forces the use of a model in which hydrogen transfer always occurs by tunneling, rather than a possible combi-nation of over barrier and through barrier transfers. Environmentally coupled tunneling assumes that protein or solvent fluctuations generate a reactive configuration along the heavy-atom coordinate, Qenv, at which hydrogen tunnels along the hydrogen coordinate, qH (Fig. 2). Such models resemble the Marcus ET model, and have been presented by several workers [12–15]. Thermal energy is required to allow the protein (or environment) to attain a reactive configuration, which leads to a temperature dependent rate (Eact „ 0). This environmental deforma-tion is largely isotope independent, although tunneling to or from an excited hydrogen vibrational level can lead to some isotope dependence [6,15,17]. The KIE arises from the differential tunneling probabilities of H and D at the reactive configuration, and reflects the barrier to tunneling along the hydrogen coordinate. These tunneling models additionally posit an environmental vibration (gating) that modulates the width of the tunneling barrier, and leads to a temperature dependent KIE. This is due to a compromise between an increased tunneling probability at short transfer distances and the energetic cost of decreasing the tunneling barrier. These features directly link enzyme fluctuations to the reaction coordinate, making a quantum view of H trans-fer necessarily a dynamic view of catalysis. AN ENVIRONMENTALLY COUPLED TUNNELING MODEL Environmentally coupled hydrogen tunneling models can accommodate the composite kinetic data for WT-SLO and its mutants [6], and are a promising general treatment for Ó FEBS 2002 Hydrogen tunneling and protein dynamics (Eur. J. Biochem. 269) 3117 probability of tunneling must account for the energy (Ex) required to change the distance between the potential wells. The KIE expression (Eqn 2) shows how the tunneling overlap (F.C.Term) can be modulated by the gating vibration in a temperature dependent fashion, where kb is Boltzmann’s constant, r0 is the equilibrium separation, and r1 is the final separation of the potential wells. F:C:TermH F:C:TermD r0 expðmHxHr2 =22ÞexpðEX=kbTÞdX r1 expðmDxDr2 =22ÞexpðEX=kbTÞdX ð2Þ Fig. 2. Energy surface for environmentally coupled hydrogen tunneling. (Top) Environmental free energy surface, Qenv, with the free energy of reaction (DG°) and reorganization energy (k) indicated. (Bottom) hydrogen potential energy surface, qH, at different environmental configurations. R0 is the reactant configuration, à denotes the reactive configuration, and P0 is the product configuration. Gating also alters the distance (Dr) of hydrogen transfer (see text). hydrogen tunneling in enzymes. The model of Kuznetsov and Ulstrup [15] was used to account for the variable-temperature KIE data of WT-SLO and its mutants [6]. In this model, the rate for H• tunneling is governed by an isotope-independent term (const.), and an environmental energy term relating k, the reorganization energy, to DG°, thedrivingforceforthereaction(Eqn1),whereRandTare thegasconstantandabsolutetemperature,respectively.The Franck–Condon nuclear overlap along the hydrogen coordinate (F.C.Term) is the weighted hydrogen tunneling probability. n o ktun ¼ ðconst.Þexp ðDGo þ kÞ2=ð4kRTÞ ðF.C.TermÞ ð1Þ The F.C.Term arises from the overlap between the initial and final states of the hydrogen’s wave function and, consequently, depends on the thermal population of each vibration level. In comparing H to D, the shorter deBroglie wavelength for D is indicative of a more localized wavefunction and, thus, a smaller F.C.Term. In the simplifying limit in which only the lowest vibration level is populated, the F.C.Term will be temperature independent. In practice, thermal population of excited vibration levels leads to a slight temperature dependence to the KIE, as the C-D stretch has smaller vibrational quanta than the C-H stretch ( 2200 cm)1 vs. 3000 cm)1). The factors that contribute to the Franck–Condon overlap are the frequency of the reacting bond (xH or xD),themass(mH ormD)ofthetransferredparticle,andthe distance over which H or D tunnels. When environmental vibrations(gating)modulatethisdistance,thentheresultant According to Eqn (2), the energetic cost of gating (EX ¼ ½2xXX ) contains 2 (Planck’s constant divided by 2p), the frequency of the gating oscillation (xX), and the gating coordinate (X ¼ rX mXxX=2). This latter term depends on the distance over which the gating unit moves (rX), together with the gating frequency (xX) and its mass (mX). Gating modulates the tunnel barrier by altering the hydrogen transfer distance from an equilibrium distance (r0) to a shorter distance (r1); assuming that the gating motion linearly reduces the hydrogen donor–acceptor separation,thenthedistanceofhydrogentransferisreduced by the distance of gating (rH,D ¼ r0 ) rX). Importantly, the interplay between the F.C.Term and the gating energy leads to a different distance of transfer for the light and heavy isotopes (rD < rH). This latter property can lead to an extremely temperature dependent KIE. VARIABLE TEMPERATURE KIES IN AN ENVIRONMENTALLY COUPLED TUNNELING MODEL The above model predicts that the magnitude of the KIE reflects the tunneling barrier (primarily the transfer dis-tance), while the temperature dependence of the KIE principally reflects gating (EX). Near ambient temperatures, nearly temperature independent KIEs result when gating is energetically too costly to bethermally active(2xX kbT), with the KIE becoming progressively more temperature dependent when gating becomes thermally active (2xX < kbT) (Fig. 3). In the absence of gating, the energetic barrier to hydrogen transfer comes from the exponential term in Eqn (1) (designated environmental reorganization, or ÔpassiveÕ dynamics). Gating increases the barrier to reaction further due to the second exponential termin Eqn (2)(designatedgating,orÔactiveÕdynamics)[6]. An interpretation of hydrogen tunneling behavior based upon this environmentally coupled tunneling model was presented in a recent publication [6], and is summarized below. This full-tunneling model leads to a range of temperature dependencies for the KIEs, which reflect the extenttowhichgating modulatesthedistanceofH transfer. This is in contrast to a static model, presented earlier, that relied on a tunneling correction to a semiclassical reaction [4]. According to the environmentally coupled tunneling model, when 2xX kbT the gating vibration does not modulate the tunneling distance appreciably, producing a nearly temperature independent tunneling distance, and hence a temperature independent KIE. Note that under conditions where AH/AD 1, there can be an appreciable temperature dependence to the rates, arising from the ... - tailieumienphi.vn