A critical test of the tunneling and coupled motion concept in enzymatic alcohol oxidation

Article abstract of DOI:10.1021/ja405917m

The physical mechanism of C-H bond activation by enzymes is the subject of intense study, and we have tested the predictions of two competing models for C-H activation in the context of alcohol dehydrogenase. The kinetic isotope effects (KIEs) in this enzyme have previously suggested a model of quantum mechanical tunneling and coupled motion of primary (1) and secondary (2) hydrogens. Here we measure the 2 H/T KIEs with both H and D at the 1 position and find that the 2 KIE is significantly deflated with D-transfer, consistent with the predictions of recent Marcus-like models of H-transfer. The results suggest that the fast dynamics of H-tunneling result in a 1 isotope effect on the structure of the tunneling ready state: the trajectory of D-transfer goes through a shorter donor-acceptor distance than that of H-transfer.

Full text of DOI:10.1021/ja405917m

Communication
pubs.acs.org/JACS
A Critical Test of the “Tunneling and Coupled Motion” Concept in
Enzymatic Alcohol Oxidation
Daniel Roston† and Amnon Kohen*
Department of Chemistry, University of Iowa, Iowa City, Iowa 52242, United States
S
* Supporting Information
ABSTRACT: The physical mechanism of C−H bond
activation by enzymes is the subject of intense study, and
we have tested the predictions of two competing models
for C−H activation in the context of alcohol dehydrogen-
Figure 1. Schematic illustration of the differences between the two
ase. The kinetic isotope effects (KIEs) in this enzyme have
models in question: (a) Traditional model of tunneling and coupled
previously suggested a model of quantum mechanical
motion, where the arrows represent the coupled motion of the 1° and
tunneling and coupled motion of primary (1°) and
two 2° hydrogens at the TS. As these three atoms constitute a normal
secondary (2°) hydrogens. Here we measure the 2° H/T
KIEs with both H and D at the 1° position and find that
mode, isotopic substitution of any of them will alter the KIE on the
others. (b) By the proposed model, since H’s wave function is more
the 2° KIE is significantly deflated with D-transfer,
consistent with the predictions of recent Marcus-like
models of H-transfer. The results suggest that the fast
dynamics of H-tunneling result in a 1° isotope effect on
the structure of the tunneling ready state: the trajectory of
D-transfer goes through a shorter donor−acceptor
distance than that of H-transfer.
diffuse than D’s, its TRS (see Figure 2) is more “dissociated”. The
double-headed arrows represent the change in vibrational ZPE from
ground state to TRS, which determine the 2° KIEs. (c) Since D’s wave
function is more localized than H at the TRS, its TRS is more
“associated”, leading to suppression of the change in vibrational ZPE
from ground state to TRS and thus deflated 2° KIEs.
significant predictions, that Swain−Schaad exponents (SSEs)
would be inflated. The SSE is the relationship between KIEs
using different combinations of isotopes of hydrogen.9 A simple
derivation making the assumptions of semiclassical transition-
state theory, no tunneling, and harmonic vibrational frequencies
showed that the SSE should be a constant, regardless of what
reaction is studied or which atom is isotopically labeled:9
lcohol dehydrogenase (ADH) is an important model
Asystem for studying the physical processes involved in
enzyme-catalyzed hydrogen transfers. ADH catalyzes the
oxidation of alcohol using a nicotinamide cofactor (Scheme
1), and this reaction has provided many surprising experimental
results that have caused the enzymology community to rethink
many facets of enzymology.1,2
kH
ln
(k )
T
SSE =
= 3.3
kD
a
Scheme 1. Reaction Catalyzed by ADH
ln
(k )
(1)
T
where ki is the rate with isotope i. Since Klinman and co-
workers found that the relationship was extraordinarily inflated
for 2° KIEs in yeast ADH (yADH),8 inflated SSEs have been
cited prolifically as evidence for tunneling and coupled
motion.1,10 Computational studies11,12 provided the first
quantitative explanation of KIEs in ADH, as well as additional
insights into the reaction, although these studies focused on the
horse ADH, where kinetic complexity masks the intrinsic KIEs
and mSSEs.13
a
Using benzyl alcohol as an alternative substrate. R = adenine
diphosphate ribosyl.
Perhaps due to the relative ease of synthesizing the necessary
isotopically labeled materials, the particular experiments that
showed the inflated 2° SSEs (in yeast8 as well as other
ADHs14,15) were mixed-labeling experiments,16 where the 2°
H/T KIE was measured with H at the 1° position, but the 2°
D/T KIE was measured with D at the 1° position. Thus, the
experiments measured the mixed-labeling 2° SSE (mSSE):
One of the most significant concepts to come out of work on
ADH is the notion of “quantum mechanical tunneling and
coupled motion” between primary (1°) and secondary (2°)
hydrogens. The theory of tunneling and coupled motion
(Figure 1a) posits that the reaction coordinate for hydride
transfer involves motion of both the 1° and 2° hydrogens and
that together the hydrogens tunnel through the reaction
barrier.3−7 At its time, this concept seemed to be in accordance
with some surprising KIE data, and additional KIE experi-
ments8 apparently confirmed one of the model’s most
Received: June 12, 2013
© XXXX American Chemical Society
A
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Figure 2. Marcus-like model of H-tunneling. (A) Top, middle, and bottom panels show three stages of the reaction in two designated coordinates:
the H position and the positions of the heavy atoms that modulate the potential surfaces (reactant surface is blue and product surface is red) for the
transferred H. In the top panel, the heavy atoms are in a position such that the ZPE of the H is lower in the reactant well, so the H-wave function
(green) is localized there. In the middle panel, the heavy atoms have rearranged to a TRS (‡), where the ZPE for the transferred H is equal in the
reactant and product wells and the H-wave function (including contributions from any motions coupled to the H-position) can tunnel through the
barrier. The rate of reaching this tunneling ready state depends on the reaction driving force (ΔG°) and the reorganization energy (λ). In the bottom
panel, the heavy atoms have rearranged further, making the ZPE of the product lower than the reactant and thus trapping the transferred H in the
product well. (B) At the TRS (middle panel of A) fluctuations of the DAD affect the tunneling probability. The top panel shows a free energy surface
for the designated DAD coordinate, indicating the different levels of reactant−product wave function overlap at different DADs. At short enough
DAD, the ZPE of the transferred particle may be above the barrier, but this leads to very small 1° KIEs and does not appear to be the case for ADH.
The middle panel shows the Boltzmann probability distribution of the system being at any given DAD (magenta), along with the tunneling
probabilities of H and D as a function of DAD (orange and purple, respectively). The bottom panel shows the product of the Boltzmann factor and
the tunneling probability for each particle, yielding the probability of a reactive trajectory as a function of DAD. Panel B illustrates that the reactive
trajectories for H and D go through different average DADs, constituting an isotope effect on TRS structure. In ADH, the difference in average DAD
for hydride vs deuteride transfers, which was estimated as 0.2 Å, leads to differences in 2° KIEs when the transferred isotope is different.22
kHH
transfer, which is a component of large-curvature tunneling
models.23 It is important to note that ref 24 indicated that the
theoretical treatment of such reactions by Truhlar and Gao
encapsulates all the components of the Marcus-like models and
does not contradict such phenomenological models. In addition
to increased steric hindrance, at the shorter DAD the
transferred particle is less delocalized (the donor and acceptor
wells are closer to one another), so the probability density of
that particle in the vicinity of the 2° hydrogen is increased,
leading to larger zero point energy (ZPE) and smaller KIEs at
the 2° position. These calculations were based on Marcus-like
models of hydrogen tunneling (Figure 2), which have found
great use in rationalizing both 2° and 1° KIEs and their
temperature dependence.25−31 Marcus-like models explain C−
H activation in terms of a separation between heavy atom
motion and hydrogen tunneling and give a rate constant (k) of
the form:
ln
ln
(k )
HT
mSSE =
kDD
(k )
(2)
DT
where kij is the rate with isotope i at the 1° position and isotope
j at the 2° position. According to semiclassical transition-state
theory and the Bigeleisen equation,17 the mSSE should equal
the SSE, since the rule of the geometric mean (RGM) states
that there are no isotope effects on isotope effects.18,19
Nonetheless, one of the great mysteries has been why inflated
SSEs have appeared in so few other systems,20 despite evidence
that tunneling is important to most or all H-transfers.
An analysis of the inflated mSSEs from many different ADHs
showed that the source of the inflation was not that the 2° H/T
KIE was inflated, as expected from the traditional model of
tunneling and coupled motion, but that the D/T KIEs were
deflated.21 The data suggested that the shorter donor−acceptor
distance (DAD) necessary for D-tunneling caused steric
hindrance between the substrates to inhibit rehybridization of
the donor carbon, thus deflating the 2° KIEs. A recent
experimental study of the yADH reverse reaction led to QM
calculations that explained all 2° KIEs and most other data on
the C−H activation for this enzyme.22 A critical component in
these calculations was a shorter DAD for D-transfer than for H-
|V|2
ℏ
π
λkBT
∞
2
°
B
B
k =
e−(ΔG +λ) /4k Tλ
F(m, DAD)e−E(DAD)/k TdDAD
∫
0
(3)
The factors in front of the integral give the rate of reaching a
tunneling ready state (TRS) based on the electronic coupling
between reactants and products (V), the reaction driving force
(ΔG°), and the reorganization energy (λ). A TRS is a point of
B
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Communication
transient degeneracy between reactants and products, where
the H can tunnel while still conserving energy. The process of
reaching a TRS is depicted in Figure 2a. The integral computes
the probability of transmission to products once the system
reaches a TRS (Figure 2b). This probability is based on the
probability of tunneling as a function of mass and DAD,
F(m,DAD), and a Boltzmann factor giving the probability of
being at any given DAD. Integrating over all DADs gives the
overall probability of transmission to products. The free energy
surface dictating the reaction depends on the nature of the
substrates as well as the enzyme environment, though we note
that eq 3 assumes thermal equilibrium (i.e., no nonstatistical
dynamics). This kind of model proposes that all isotopes of H
react by tunneling but expects that the trajectory of heavier
isotopes will pass through a shorter DAD (Figure 2b).
So far, all the experimental evidence supporting this
explanation was quite complex and thus indirect.3,8,14,15,22,32,33
Here we have conducted one of the simplest possible tests of
the predictions of that model: we have measured the 2° H/T
KIEs on the oxidation of benzyl alcohol with both H- and D-
transfer (Table 1). This experiment directly tests the effect of
models that have dispensed with some simplifying assump-
tions.16,36,37
This measurement directly confirms that the inflated mSSE
comes from a deflation of 2° KIEs when D is at the 1° position,
as originally suggested in ref 21. Furthermore, this measure-
ment reveals that the deflation of the 2° KIEs with D-transfer is
not unique to D/T KIEs, as observed before, but is a general
phenomenon reflecting the suppression of donor rehybridiza-
tion at the TRS due to the close proximity of the H-acceptor.
Both refs 34 (using a truncated Bell correction)38 and 22 (using
a Marcus-like model) suggested a critical role for H-tunneling
in predicting this breakdown of the RGM, and the two studies
made similar predictions for the value of the 2° H/T KIE with
D-transfer, which we have measured here for the first time
(Table 1). Nonetheless, the Marcus-like model has several
advantages. First, the Bell-type corrections used in early models
of tunneling and coupled motion5,7,34,39 cannot account for
temperature-independent KIEs when reaction rates are temper-
ature dependent.10,14,40 This, however, is precisely the observed
behavior of many enzyme reactions,1,2,41 including that of a
thermophilic ADH, which also showed inflated mSSEs.14 In
fact, ref 34 stated explicitly that the temperature dependence of
KIEs in that model was steeper than the observed data.8
Additionally, the nature of the coupling between vibrational
modes in that study was vague and difficult to interpret. Thus,
the more recent Marcus-like model that can account for all of
the behavior of these reactions within an intuitively satisfying
model is more compelling.
Marcus-like models originally arose out of the need to
explain the temperature dependence of 1° KIEs,25−29 but they
describe a mechanism for C−H bond activation which, if right,
should also account for 2° KIEs. Thus far, though, very little
work has attempted to test the predictions of Marcus-like
models in the context of 2° KIEs.21,22,42 The experiments here
directly demonstrate the deflation of 2° KIEs for D-transfer
relative to H-transfer. Since the current experiment does not
involve mixed labeling, it directly reveals the source of one of
the most puzzling results for 2° KIEs (inflated mSSEs) and
contributes strong support for the mechanism of C−H
activation described by Marcus-like models. In this mechanism,
H-tunneling is modulated by the “heavy atoms” coordinate that
tunes the transient degeneracy necessary for tunneling. Once
degeneracy is achieved, the transferred atom can tunnel to
products with efficiency dependent on its mass and the DAD.
Since the DAD must be shorter for D to tunnel than for H to
tunnel, the average DAD of transfer is shorter with D than with
H (Figure 2b).
Table 1. 2° KIEs and SSEs on Oxidation of Benzyl Alcohol
by yADH
d
e
measured
predicted
predicted
a
k
DH/kDT
1.18 0.03
1.11
1.32
1.03
9.4
1.12
1.33
1.04
7.7
a b
&
k
HH/kHT
DD/kDT
1.30 0.02
1.03 0.01
8.9 3.0
c
k
mSSE
SSED
5.6 2.0
3.4
2.9
a
b
This work. Also measured in refs 8 and 33, and all measurements are
c
d
e
within error of one another. Ref 8. Ref 22. Ref 34.
the 1° (transferred) isotope on the 2° KIEs (the RGM) without
the many possible effects of assessing it from mixed labeling
measurements (eqs 2 and 4). The usefulness of directly
measuring kDH/kDT was initially suggested by simple calcu-
lations of coupling between the 1° and 2° C−H bonds34 but
has not yet been attempted experimentally due to the required
stereospecific labeling pattern. The new measurement was
made possible by the chemoenzymatic synthesis of 7R-[2H]-
phenyl-[14C]-benzyl alcohol, which had previously been
attempted for over 10 years (see Supporting Information and
ref 35). We measured the KIEs competitively using the same
conditions as in previous studies on yADH (25 °C, pH 8.5),8,32
and the results (Table 1) are qualitatively consistent with the
predictions based on both 1°-2° coupled motion34 and Marcus-
like models.21,22 Specifically, the 2° KIE is significantly deflated
with D- vs H-transfer (1.30 0.02 and 1.18 0.03 with H- and
D-transfer, respectively). Together with the value of the 2° D/
T KIE with D-transfer (1.03 0.01),8 our measurements yield
the SSED:
In summary, the ADH reaction with H-transfer effectively
goes through a different TRS than the reaction with D-transfer.
The electronic potential surface is the same for the two
reactions, consistent with the Born−Oppenheimer approxima-
tion, but the dynamics of nuclear tunneling contribute to the
reaction’s bottleneck (i.e., the point along the reaction
coordinate with the lowest flux of forward trajectories,
analogous to the variational transition state).24,43 One can
describe this result as an isotope effect on the structure of the
TRS. In a general sense, it is perhaps not surprising that the
dynamics of H-tunneling contribute to the rate limitation of the
H-transfer step, but here we have demonstrated clearly that this
dynamic bottleneck44 has important implications for the
structure of the TRS. Furthermore, we have shown that 2°
KIEs provide important information to determine the structure
of a TRS. In contrast to 1° KIEs though, 2° KIEs are only
kDH
ln
(k )
DT
SSED =
kDD
ln
(k )
(4)
DT
where, as in eq 2, kij is the rate with isotope i at the 1° position
and isotope j at the 2° position. The value we obtain for SSED
(5.6
2.0) is slightly higher than values calculated for the
SSED,22,34 but it is within the (larger) range calculated by
C
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Journal of the American Chemical Society
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(23) Kreevoy, M. M.; Ostovic, D.; Truhlar, D. G.; Garrett, B. C. J.
Phys. Chem. 1986, 90, 3766.
indirectly affected by tunneling: they are a manifestation of
isotopic differences in the structural rearrangement necessary to
reach the TRS (differences in ZPE contributions to ΔG° and λ
of eq 3). The structural information provided by 2° KIEs has
been very useful in developing powerful transition-state analog
inhibitors for enzymes that catalyze heavy atom bond
cleavages,45 and now the door is open to use analogous
methods for enzymes that catalyze H-transfers.
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ASSOCIATED CONTENT
* Supporting Information
Detailed experimental methods and additional results are
available. This material is available free of charge via the
Internet at http://pubs.acs.org.
■
S
(33) Welsh, K. M.; Creighton, D. J.; Klinman, J. P. Biochemistry 1980,
19, 2005.
AUTHOR INFORMATION
(34) Rucker, J.; Klinman, J. P. J. Am. Chem. Soc. 1999, 121, 1997.
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London, 1980.
■
Corresponding Author
amnon-kohen@uiowa.edu
Present Address
†Department of Chemistry, University of Wisconsin, Madison,
WI 53706
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(41) Hay, S.; Sutcliffe, M. J.; Scrutton, N. S. In Quantum Tunnelling in
Enzyme-Catalysed Reactions; Allemann, R. K., Scrutton, N. S., Eds.;
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Notes
The authors declare no competing financial interest.
ACKNOWLEDGMENTS
■
This work was supported by grants to A.K. from the NIH
(R01GM65368) and NSF (CHE-1149023). D.R. was sup-
ported by a predoctoral fellowship from the NIH (T32
GM008365). The authors are grateful to Bryce Plapp for his
assistance in the production of the yADH and for fruitful
discussions.
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