MINIREVIEW Environmentally coupled hydrogen tunneling Linking catalysis to dynamics Michael J. Knapp 1 and Judith P. Klinman 1,2 1 Department of Chemistry and 2 Department 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 aretoolarge(k H /k D > 7) and/or exhibit unusual tempera- ture dependence such that the Arrhenius prefactor KIEs (A H /A D ) 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- tum 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 A H /A D values, which reflect the extent to which gating modulates hydrogen transfer. Gating is the primary determinant of the tem- perature 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 tempera- ture KIEs as a direct probe of coupling between environ- mental 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 dehy- drogenase and soybean lipoxygenase-1. Keywords: hydrogen tunneling; kinetic isotope effects; lip- oxygenase; protein dynamics; reaction coordinate. INTRODUCTION Quantum effects have long been appreciated in biological electron transfer (ET) reactions, due to the large uncertainty in position for the e – . The quantum nature of ET has required new reaction models that go beyond transition-state theory. Marcus recognized the contribution of heavy-atom coordi- nates to the rate of ET through an environmental energy term ðk ET / e ÀDG z =RT Þ,whereDG à is the free energy barrier to reaction, R is the gas constant, and T is absolute temperature [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 remarkable insight is in stark contrast to typical assumptions 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/ ffiffiffiffiffiffiffiffiffi 2mE p ,inwhichh is Planck’s constant, m is the mass of the particle, and E is its energy. Assuming an energy of 20 kJÆmol )1 (% 5kcalÆ mol )1 ) the deBroglie wavelength is calculated to be 0.63 A ˚ and 0.45 A ˚ for protium (H, or 1 H) and deuterium (D, or 2 H), respectively. As hydrogen is typically transferred over a similar distance (< 1 A ˚ ), this positional uncertainty is significant, and implicates considerable nonclassical proper- ties for hydrogen transfers. Despite the underlying quantum nature of hydrogen transfer, such reactions frequently mimic classical reactions (as by exhibiting a positive temperature dependence); for this reason, hydrogen tunnel- ing has typically been treated as a perturbation of transition- state theory (TST) [16,17]. While TST remains the common language of chemical reactions, increasing numbers of workers are coming to 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; D k cat , kinetic isotope effect on k cat ; 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) Eur. J. Biochem. 269, 3113–3121 (2002) Ó FEBS 2002 doi:10.1046/j.1432-1033.2002.03022.x 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, in that activated complex theory formulates the rate of a reaction as ðk TST ¼ Ae ÀDG z =RT Þ,inwhichA is a pre- exponential term, and DG à is the energetic barrier to reaction. It is natural to focus attention on the exponential term, as a relatively small change in DG à leads to a large change in k TST .ReducingDG à canbeachievedbyeither stabilizing the transition-state, or by ground-state destabil- ization; both lead to a similar reduction in DG à ,and significant alterations in k TST . 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 k H ¼ A H exp {–(DG à ) ½hm H )/RT}, where m H 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 k H /k D ¼ (A H /A D ) exp{(½hm H ) ½hm D )/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 (% 7at 300 K), which vanishes at infinite temperature, as A H / A D % 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 to explain some of the peculiar behavior of organic reactions 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 (A H /A D <1)as measured by variable-temperature KIEs (VT-KIEs) [26]. Additionally, the exponent relating the three hydrogen isotopes (H/T vs. D/T) has a characteristic value in the semiclassical model [k H /k T ¼ (k D /k T ) 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 [k H /k T >(k D /k T ) 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 (A H /A D ( 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° A H /A D ratios which deviated from unity in the proton (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. 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) DG à is the free energy barrier to hydrogen transfer, ½hm H and ½hm D 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. 3114 M. J. Knapp and J. P. Klinman (Eur. J. Biochem. 269) Ó FEBS 2002 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 reported by this lab [3, 6, 7], and by Scrutton and 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- torratios(A H /A D ) 1) and finite activation energies (E act „ 0) that are incompatible with the Bell model [6,7]. Furthermore, the A H /A D ratios were observed to become inverse upon perturbing the system, with the perturbant being temperature in ht-ADH, and site-specific mutagenesis in SLO. As discussed below, a wide variation in A H /A D can, in fact, be explained as arising from alterations in the environmental dynamics that modulate hydrogen tunneling. The physiological temperature of B. stearothermophilus is 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 increased as a function of temperature, contrary to standard 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 k cat exhibited an increased activation energy. Below 30 °C, the 1° KIEs exhibit an inverse A H /A D ratio (A H /A D ¼ 1 · 10 )5 ), whereas the KIEs above 30 °C show an A H /A D ratio greater than unity (A H /A D ¼ 2). Sizeable activation energies, together with inverse Arrhenius 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 one treat the enzyme as if it exists in two phases separated by 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- thebarrier.Above30°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 any tunneling-correction model [3,31–33]. The H/D KIE for the H• transfer of WT-SLO is greater than 80 at room temperature, and the activation energy on H• transfer is remarkably small (E act ¼ 2.1 kcalÆmol )1 ) [9,34–36]. When this result was reported, it signaled a new era in hydrogen transfer chemistry, as it was so deviant as to make tunneling corrections of dubious relevance. Explicit tunneling effects are required to accommodate the kinetics of SLO, and may be equally important in 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 of the pro-S hydrogen from C11 of LA by the Fe 3+ -OH cofactor, forming a substrate-derived radical intermediate and Fe 2+ -OH 2 [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 k cat ( D k cat ) 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 other investigations have confirmed the finding that the KIE on the chemical step of SLO is %80 at room temperature [6,35], including one notable study that excluded magnetic effects as the origin of this KIE [36]. Potential complications in assigning D k cat to a single chemical step, for example due to a branched reaction mechanism, were also ruled out [34]. Scheme 1. Ó FEBS 2002 Hydrogen tunneling and protein dynamics (Eur. J. Biochem. 269) 3115 All data indicate that the chemical step (H• abstraction) is fully rate-limiting on k cat , in WT-SLO, and that the steady- state KIE ( D k cat ) 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 (DH à ¼ 1.5 kcalÆmol )1 ) is much less than the entropic barrier (–TDS à 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 (A H /A D 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 semiclassical theory of KIEs. It is clear that the semiclassical 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 Fe 3+ -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 (A H /A D ¼ 18), the two mutations closest to the reacting position, Leu546 fi Ala, Leu754 fi Ala, change the tem- perature-dependence of the KIE (A H /A D 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 significantly more temperature dependent than in WT-SLO, leading to an inverse Arrhenius prefactor KIE (A H /A D 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 ( D k cat > 80) for each mutant, indicating similar tunneling components for all reactions. From the outset it appeared that a tunneling correction would be unable to account for the magnitude of the KIE in 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 A H /A D ratio observed in SLO as a function of mutation. A previous formalism of tunneling advanced by this lab relied upon the A H /A D 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 (A H /A D ) 1) approximates deep tunneling behavior (H and D tunnel similarly), that Ile553 fi Ala (A H /A D ( 1) exhibits moderate tunneling (H tunnels more than D), and that Leu546 fi Ala and Leu754 fi Ala (A H /A D % 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 E act values would be accompanied by large A H /A D ratios, yet the Ile553 fi Ala mutant has a small E act value and a small A H /A D 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 A H /A D >1to A H /A D < 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 (k H /k D >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, Q env , at which hydrogen tunnels along the hydrogen coordinate, q H (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 (E act „ 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 Table 1. Kinetic parameters for SLO and mutants in pH 9.0 borate buffer. Data were collected between 5 °Cand50°C. Standard errors from data fitting are in parentheses. k cat a (s –1 ) KIE b E act (kcalÆmol –1 ) DE act c (kcalÆmol –1 )A H /A D WT-SLO 297 (12) 81 (5) 2.1 (0.2) 0.9 (0.2) 18 (5) Leu546 fi Ala 4.8 (0.6) 93 (9) 4.1 (0.4) 1.9 (0.6) 4 (4) Leu754 fi Ala 0.31 (0.02) 112 (11) 4.1 (0.3) 2.0 (0.5) 3 (3) Ile553 fi Ala 280 (10) 93 (4) 1.9 (0.2) 4.0 (0.3) 0.12 (0.06) a The rate constants (k cat for 1 H 31 -LA) are reported for 30 °C. b KIE ¼ D k cat , reported for 30 °C. c This is the isotope effect on E act , DE act ¼ E act D ) E act H. 3116 M. J. Knapp and J. P. Klinman (Eur. J. Biochem. 269) Ó FEBS 2002 hydrogen tunneling in enzymes. The model of Kuznetsov andUlstrup[15]wasusedtoaccountforthevariable- 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 ° , the driving force for the reaction (Eqn 1), where R and T are the gas constant and absolute temperature, respectively. The Franck–Condon nuclear overlap along the hydrogen coordinate (F.C.Term) is the weighted hydrogen tunneling probability. k tun ¼ðconst.Þexp ÀðDG o þ kÞ 2 =ð4kRTÞ no ÂðF.C.TermÞð1Þ 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 (x H or x D ), the mass (m H or m D ) of the transferred particle, and the distance over which H or D tunnels. When environmental vibrations (gating) modulate this distance, then the resultant probability of tunneling must account for the energy (E x ) 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 k b is Boltzmann’s constant, r 0 is the equilibrium separation, and r 1 is the final separation of the potential wells. KIE ¼ F:C:Term H F:C:Term D ¼ R r 0 r 1 expðÀm H x H r 2 H =22ÞexpðÀE X =k b TÞdX R r 0 r 1 expðÀm D x D r 2 D =22ÞexpðÀE X =k b TÞdX ð2Þ According to Eqn (2), the energetic cost of gating (E X ¼ ½2x X X 2 ) contains 2 (Planck’s constant divided by 2p), the frequency of the gating oscillation (x X ), and the gating coordinate (X ¼ r X ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi m X x X =2 p ). This latter term depends on the distance over which the gating unit moves (r X ), together with the gating frequency (x X )anditsmass(m X ). Gating modulates the tunnel barrier by altering the hydrogen transfer distance from an equilibrium distance (r 0 ) to a shorter distance (r 1 ); assuming that the gating motion linearly reduces the hydrogen donor–acceptor separation, then the distance of hydrogen transfer is reduced by the distance of gating (r H,D ¼ r 0 ) r X ). 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 (r D < r H ). 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 (E X ). Near ambient temperatures, nearly temperature independent KIEs result when gating is energetically too costly to be thermally active (2x X ) k b T), with the KIE becoming progressively more temperature dependent when gating becomes thermally active (2x X < k b T) (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 term in Eqn (2) (designated gating, or ÔactiveÕ dynamics) [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 extent to which gating modulates the distance of H 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 2x X ) k b T 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 A H /A D ) 1, there can be an appreciable temperature dependence to the rates, arising from the Fig. 2. Energy surface for environmentally coupled hydrogen tunneling. (Top) Environmental free energy surface, Q env , with the free energy of reaction (DG°) and reorganization energy (k) indicated. (Bottom) hydrogen potential energy surface, q H , at different environmental configurations. R 0 is the reactant configuration, à denotes the reactive configuration, and P 0 is the product configuration. Gating also alters the distance (Dr) of hydrogen transfer (see text). Ó FEBS 2002 Hydrogen tunneling and protein dynamics (Eur. J. Biochem. 269) 3117 passive dynamics term. In the static model, temperature independent KIEs are also predicted, but only under conditions where the activation energy approaches zero [4]. As the gating energy decreases (2x x % k b T), gating becomes more effective at modulating the tunneling prob- ability, leading to more temperature dependent KIEs and to values for A H /A D that decrease and may pass through unity. Under these conditions, the activation energy for hydrogen transfer is governed by both passive and active dynamics. As the frequency for gating decreases further (2x X < k b T), gating becomes the dominant feature of the reaction coordinate, and KIEs become increasingly tem- perature dependent such that A H /A D < 1 is predicted. Finally, when 2x X ( k b T, extensive environmental dynamics lead to smaller KIEs that follow the classical prediction, with A H /A D ¼ 1. Correlating molecular motions with enhanced rates is the Ôholy grailÕ of much current research into catalysis. The environmentally coupled tunneling model indicates how KIEs can provide a link between catalysis and dynamics. Independent physical probes of protein dynamics can be problematic, in that the measured dynamic parameters may not be correlated with specific motions that effect catalysis; additionally, these may detect global, rather than local, effects. For example, the measurement of amide exchange rates (as for ht-ADH [30]) probes the global accessibility of amides to proton exchange. One intriguing technique combines H/D exchange of amides with proteolysis; this provides a measure of more local amide exchange rates, as carried out recently for extracellular regulated protein kinase-2 [39]. A weakness of the amide exchange technique is uncertainty regarding the mechanism of exchange, and many workers consider amide exchange as indicative of protein flexibility rather than dynamics [40–42]. NMR techniques are of great use in smaller proteins, and some progress has been made in studying how protein motions contribute to ligand binding [43]. Unfortunately, the large size of SLO (94 kDa) precludes the use of standard NMR techniques. Optical techniques, such as tryptophan phos- phorescence, appear to be promising ways of probing environmental oscillations near interior tryptophan residues [44]. Once the motion of protein functional groups has been well described, the possible relationship of this motion to the reaction coordinate would still need to be determined. Molecular dynamics calculations, to search for coupling between environmental oscillations and hydrogen transfer reactions, are providing some insight into this problem [11,21,45]. RELATIONSHIP TO OTHER TUNNELING MODELS As described above, SLO catalyzes a reaction that proceeds by nuclear tunneling. Any attempt at modeling H• transfer as tunneling through a static barrier predicts an enormous KIE % 10 4 (assuming a typical H• transfer barrier) that is fully temperature independent [46]. Additionally, a static tunneling model predicts a temperature independent rate (E act ¼ 0). Clearly a static model for hydrogen tunneling is inadequate to describe H• tunneling in SLO, whereas the environmentally coupled tunneling model is a realistic approach to describe this enzymatic H• transfers (Table 2). Fig. 3. (A) Calculated rates for H and D transfer by environmen- tally coupled tunneling as a function of gating energy at 303 K, (B) cal- culated kinetic isotope effects (k H /k D ) and (C) Arrhenius prefactor kinetic isotope effects (A H /A D ). (A) This calculation allowed for the thermal population of excited C-H and C-D stretches, and for tran- sitions to excited vibrational levels. The following parameters were used: DG° ¼ )6kcalÆmol )1 , k ¼ 18 kcalÆmol )1 , m X ¼ 110 gÆmol )1 , r 0 ¼ 1.0 A ˚ . The gating energy was varied by changing x X .(B)Cal- culated kinetic isotope effects (k H /k D ) based upon (A). (C) Arrhenius prefactor kinetic isotope effects (A H /A D )extrapolatedfrom(B). Table 2. Observed kinetic isotope effects in SLO compared to KIEs calculated from several models. D k cat A H /A D Reference Observed KIE a 81 (5) 18 (5) [6] TST Model < 10 0.7–1.2 [17,55] Static Tunneling Model % 10 4 % 10 4 [46] Gated Tunneling Model 93 12.4 [6] a Standard errors are indicated in parentheses. 3118 M. J. Knapp and J. P. Klinman (Eur. J. Biochem. 269) Ó FEBS 2002 The vibrationally enhanced ground-state tunneling model of Bruno & Bialek (VEGST) assumes that environmental vibrations modulate the tunneling probability [14]; at its core, this model is identical to the environmentally coupled hydrogen tunneling model with the simplification that the energy levels of reactant and product are matched. Other workers have erroneously attributed the pattern of tem- perature independent KIEs and A H /A D > 1, as observed in WT-SLO, to VEGST [47]. As discussed above, the domin- ant environmental contribution in WT-SLO, as in other enzymes that exhibit nearly temperature-independent KIEs, is the environmental reorganization, which is different from a vibrationally enhanced modulation of the tunneling distance. For this reason, it seemed appropriate to us to partition environmental dynamics into two types: passive (reorganization energy) and active (gating, or vibrational enhancement). Gating of tunneling via active dynamics requires that an environmental vibration modulating the hydrogen transfer coordinate becomes thermally active (2x X < k b T), such that the amplitude of gating is sufficient to effect a change in the tunneling probability. This leads to the variable temperature KIE pattern of A H /A D <1. The model proposed by Hynes [13,48–50], and extended by Schwartz [12,21,51,52], is very similar to the environmen- tally coupled hydrogen tunneling model [14,15]. Specifically, environmental oscillations have two effects on the reaction coordinate: they allow the hydrogen vibrational levels to become degenerate, and they modulate the distance of hydrogen transfer. Schwartz refers to these latter oscillations as Ôrate-promotingÕ vibrations [12]. These models go beyond the simple picture of Eqns (1) and (2) in that they allow for zero-point energy effects in the environmental modes, and they account for more complex coupling between the promoting vibration and the tunneling probability. Thus, these models incorporate features of hydrogen transfers that Eqn (2) neglects, but at the expense of a bit more complexity. What is the significance of hydrogen-atom tunneling? Many metallo-enzymes that activate C-H bonds do so via homolytic cleavage, and these reactions often exhibit nonclassical KIEs. These enzymes include such well-known examples as the cytochromes P450 [53], in which an electrophilic ferryl species, thought to be [Fe IV ¼ O] 2+ ,is proposed to cleave C-H bonds and then hydroxylate the carbon-centered radical. This reaction exhibits elevated H/D KIEs (% 15) under ambient conditions. The iron- dependent desaturases [31], as well as methane monooxyg- enase [32], utilize a similar di-iron core that cleaves highly inert C-H bonds; these enzymes exhibit room-temperature KIEs between 14 and 100. Recent results on peptidylgly- cine-a-amidating enzyme, a copper-dependent monooxyg- enase that is very similar to dopamine-b-monooxygenase, implicate an H abstraction that proceeds via hydrogen tunneling [54]. This enzyme exhibits a moderately elevated intrinsic KIE (% 11) that is only slightly temperature dependent (A H /A D ¼ 5). It is becoming apparent that many systems exhibit KIEs whose magnitude and tempera- ture dependencies cannot be explained by tunnel-correction models, and that these should be viewed in the context of environmentally coupled hydrogen tunneling models. SECONDARY KINETIC ISOTOPE EFFECTS IN SLO All reported 2° KIEs for SLO are normal in sign and magnitude (Table 3). Various specifically labeled linoleic acid substrates have been synthesized, and used to measure multiple 2° KIEs. The substrate has several positions that are expected to change hybridization upon reaction, both the a-2° position and the 9,10,12,13 allylic/vinylic positions. The a-2° effect was measured by comparing 1 H 31 -LA with substrate that had been isotopically substituted at the a-2° position, 11-(R)-[ 2 H]LA [9]. This measurement was extremely important, as it confirmed that the observed KIE in SLO was not due to some anomalous multiplicative effect from the a-2° position. The a-2° KIE is within the range expected from semiclassical models for a change in hybridization at C-11 from sp 3 to sp 2 [9]. No theory relating 2° KIEs to a reaction coordinate dominated by tunneling has yet been advanced, so we are at a loss to describe these results in any greater detail. It would be quite interesting to measure the Swain–Schaad relationship (k H /k T vs. (k D /k T ) 3.3 at the a-2° position), to begin to develop a theory of 2° KIEs in a full tunneling model. The 2° H/T KIE at the allylic/vinylic positions has been determined using LA that had been tracer labeled with tritium at the C-9, -10, -12, -13 positions, and therefore represents an average of KIEs over these positions [3]. Further experiments are needed to understand the origin of this 2° KIE (i.e. whether it arises from one or more labeled positions). CONCLUSION TST remains a powerful language for interpreting chemical kinetics, because it provides insight and predictability into classical reaction mechanisms. In reactions such as the H• transfer of SLO, TST and attendant tunneling-correc- tions are inappropriate, and full tunneling models must be invoked. What insight can we gain from the environmen- tally coupled tunneling model applied to SLO? Importantly this model allows a distinction between passive dynamics (environmental reorganization, k)andtheactivedynamics (gating) that modulate the tunneling barrier. These two dynamical terms have different effects on the KIE and its temperature dependence, with k affecting the rate of H and D transfer to almost equal extents and with gating being the principal determinant of the temperature dependence of the KIE. Thus, this model can provide unique insight into both Table 3. Secondary kinetic isotope effects for SLO. Reported errors are in parentheses. Position of 2° label Method KIE Reference LA vs.[11-(R)- 2 H]LA a-2° Noncompetitive, 30 °C D (k cat ) ¼ 1.1 (0.06) [9] [1- 14 C]LA vs. [9,10,12,13- 3 H]LA Allylic/vinylic Competitive, 0 °C T (k cat /K M ) ¼ 1.16 (0.04) [3] [11,11- 2 H 2 ]LA vs. [ 2 H 31 ]LA Allylic/vinylic Noncompetitive, 25 °C D (k cat /K M ) ¼ 1.13 (0.36) D (k cat ) ¼ 1.10 (0.03) [3] Ó FEBS 2002 Hydrogen tunneling and protein dynamics (Eur. J. Biochem. 269) 3119 the importance and nature of dynamics in modulating the reaction coordinate. Due to the above mentioned difficulties in correlating dynamic motions in proteins with catalysis, variable temperature KIEs may be one of the few experi- mental probes for the coupling of environmental dynamics to the chemical reaction coordinate. ACKNOWLEDGEMENTS This research was supported by grants to J. P. K. from the NSF (MCB-9816791) and the NIH (GM25765), and by a postdoctoral fellowship to M. J. K. (F32-GM19843). 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Francisco, W.A., Knapp, M.J., Blackburn, N.J. & Klinman, J.P. (2002) Nature of hydrogen activation in the peptidylglycine a-amidating reaction and its relationship to protein dynamics. J. Am. Chem. Soc. in press. 55. Schneider, M.E. & Stone, M.J. (1972) Arrhenius preexponential factors of primary hydrogen kinetic isotope effects. J. Am. Chem. Soc. 94, 1517–1522. Ó FEBS 2002 Hydrogen tunneling and protein dynamics (Eur. J. Biochem. 269) 3121 . directly link enzyme fluctuations to the reaction coordinate for hydrogen transfer, making a quan- tum view of hydrogen transfer necessarily a dynamic view of catalysis. The environmentally coupled hydrogen. 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. MINIREVIEW Environmentally coupled hydrogen tunneling Linking catalysis to dynamics Michael J. Knapp 1 and Judith P. Klinman 1,2 1 Department of Chemistry and 2 Department of Molecular and Cell Biology,