The environmentally coupled hydrogen tunneling model leads to a range of magnitudes of KIEs, which reflect the tunneling barrier, and a range of AH/ADvalues, which reflect the extent to wh
Trang 1M I N I R E V I E W
Environmentally coupled hydrogen tunneling
Linking catalysis to dynamics
Michael J Knapp1and Judith P Klinman1,2
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 nonclasnonclas-sical 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 tuntun-neling 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 AH/ADvalues, 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
I N T R O D U C T I O N
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
ðkET/ eDG z =RTÞ, where DGis 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 theorexperimental-ists, 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, k¼ h/ ffiffiffiffiffiffiffiffiffi
2mE
p , 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, or1H) and deuterium (D, or
2H), 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;Dk 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)
Trang 2appreciate [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 tunnelcorrect-ing
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 appear 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
S E M I C L A S S I C A L K I N E T I C I S O T O P E
E F F E C T S A N D T U N N E L I N G
C O R R E C T I O N S
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 ðkTST¼ AeDG z =RTÞ, 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 DGleads to a large
change in kTST Reducing DG can be achieved by either
stabilizing the transition-state, or by ground-state
destabil-ization; both lead to a similar reduction in DG, 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 kH¼ AHexp
{–(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/kD¼ (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
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 (AH/AD< 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 [kH/kT¼ (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/ADratios 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) DGis 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.
Trang 3B R E A K I N G T H E T U N N E L - C O R R E C T I O N :
T H E R M O P H I L I C A L C O H O L
D E H Y D R O G E N A S E A N D S O Y B E A N
L I P O X Y G E N A S E - 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-tor ratios ( AH/AD
(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
mutagenesis in SLO As discussed below, a wide variation in
AH/ADcan, in fact, be explained as arising from alterations
in the environmental dynamics that modulate hydrogen
tunneling
The physiological temperature of B stearothermophilus is
60–70C, sufficiently high that it was possible for Kohen
et al to collect KIE data over a very wide temperature
range (5–65C) [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
30C, below which kcatexhibited an increased activation
energy Below 30C, the 1 KIEs exhibit an inverse AH/AD
ratio (AH/AD¼ 1 · 10)5), whereas the KIEs above 30C
show an AH/AD ratio greater than unity (AH/AD¼ 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 60C than at reduced temperature
(25C), 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 frozen-out below 30C, such that
hydrogen transfer is dominated by a more classical reaction
coordinate with a portion of H transfer occurring
through-the barrier Above 30C, 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 (Eact¼ 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 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 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 assigningDkcatto a single chemical step, for example due
to a branched reaction mechanism, were also ruled out [34]
Scheme 1.
Trang 4All data indicate that the chemical step (H• abstraction) is
fully rate-limiting on kcat, in WT-SLO, and that the
steady-state KIE (Dkcat) 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 (DH¼ 1.5 kcalÆmol)1)
is much less than the entropic barrier (–TDS¼ 12.8
kcalÆmol)1) Such an interpretation becomes meaningless
when the rate and KIEs are considered within the context of
TST The KIE is only weakly temperature dependent, and
when extrapolated to infinite temperature remains very
large (AH/AD¼ 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 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/AD¼ 18), the two mutations closest to the reacting
position, Leu546fi Ala, Leu754 fi Ala, change the
tem-perature-dependence of the KIE (AH/AD¼ 3) in a manner
that suggests a modest alteration in the tunneling
coordi-nate The more distal mutant, Ile553fi Ala, exhibits a KIE
significantly more temperature dependent than in WT-SLO,
leading to an inverse Arrhenius prefactor KIE
(AH/AD¼ 0.2) that implicates a fundamental change in
the tunneling coordinate Despite the alterations in the
temperature dependencies, the KIEs at 30C remain large
(Dkcat> 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
AH/ADratio 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
behavior (H and D tunnel similarly), that Ile553fi Ala
(AH/AD 1) exhibits moderate tunneling (H tunnels more
than D), and that Leu546fi 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 Eactvalues would be accompanied by large AH/AD ratios, yet the Ile553fi 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
30C) 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
A N E N V I R O N M E N T A L L Y C O U P L E D
T U N N E L I N G M O D E L
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 C and 50 C Standard errors from data fitting are in parentheses.
k cata
E act (kcalÆmol –1 )
DE actc (kcalÆmol –1 ) A H /A D
Leu754 fi Ala 0.31 (0.02) 112 (11) 4.1 (0.3) 2.0 (0.5) 3 (3)
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.
Trang 5hydrogen 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,
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
ktun¼ ðconst.Þ exp ðDGn oþ kÞ2=ð4kRTÞo
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)1vs 3000 cm)1)
The factors that contribute to the Franck–Condon
overlap are the frequency of the reacting bond (xH or
xD), the mass (mHor mD) 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 (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 kbis Boltzmann’s constant, r0is the equilibrium separation, and
r1is the final separation of the potential wells
KIE¼F:C:TermH F:C:TermD
¼
Rr0
r 1expðmHxHr2
H= 2Þ expðEX=kbTÞdX
Rr0
r 1expðmDxDr2
D= 2Þ expðEX=kbTÞdX ð2Þ According to Eqn (2), the energetic cost of gating (EX¼
½2xXX2) contains2 (Planck’s constant divided by 2p), the frequency of the gating oscillation (xX), and the gating coordinate (X ¼ rX
ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
mXxX=2
p
) 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, then the distance of hydrogen transfer is reduced
by the distance of gating (rH,D¼ 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
V A R I A B L E T E M P E R A T U R E K I E S I N A N
E N V I R O N M E N T A L L Y C O U P L E D
T U N N E L I N G M O D E L
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 be thermally active (2xX bT), 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 passive dynamics) Gating increases the barrier to reaction further due to the second exponential term in Eqn (2) (designated gating, or active 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 2xX bT 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
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, denotes the reactive
configuration, and P 0 is the product configuration Gating also alters
the distance (Dr) of hydrogen transfer (see text).
Trang 6passive 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 (2xx kbT), gating
becomes more effective at modulating the tunneling
prob-ability, leading to more temperature dependent KIEs and to
values for AH/AD 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
(2xX< kbT), gating becomes the dominant feature of the
reaction coordinate, and KIEs become increasingly
tem-perature dependent such that AH/AD< 1 is predicted Finally, when 2xX kbT, extensive environmental dynamics lead to smaller KIEs that follow the classical prediction, with AH/AD¼ 1
Correlating molecular motions with enhanced rates is the
holy grail 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]
R E L A T I O N S H I P T O O T H E R T U N N E L I N G
M O D E L S
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 104(assuming a typical H• transfer barrier) that is fully temperature independent [46] Additionally, a static tunneling model predicts a temperature independent rate (Eact¼ 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 )6 kcalÆmol )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 ) extrapolated from ( 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.
Trang 7The 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 AH/AD> 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
(2xX< kbT), 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 AH/AD< 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 rate-promoting 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 [FeIV¼ 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-monooxygmonooxyg-enase,
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 (AH/AD¼ 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
S E C O N D A R Y K I N E T I C I S O T O P E
E F F E C T S I N S L O
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 comparing1H31-LA with substrate that had been isotopically substituted at the a-2 position, 11-(R)-[2H]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 sp3 to sp2 [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 (kH/kT vs (kD/kT)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)
C O N C L U S I O N
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) and the active dynamics (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.
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] [11,11-2H 2 ]LA vs [2H 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]
Trang 8the 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 environexperi-mental dynamics
to the chemical reaction coordinate
A C K N O W L E D G E M E N T S
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) We thank Drs Matt Meyer
and Justine Roth (UCB) for many thoughtful discussions.
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