Importance of Barrier Shape in Enzyme-catalyzed
Reactions
VIBRATIONALLY ASSISTED HYDROGEN TUNNELING IN TRYPTOPHAN
TRYPTOPHYLQUINONE-DEPENDENT AMINE DEHYDROGENASES*
Jaswir
Basran
§,
Shila
Patel
§,
Michael J.
Sutcliffe¶, and
Nigel S.
Scrutton
From the
Department of Biochemistry and the
¶ Department of Chemistry, University of Leicester, University
Road, Leicester LE1 7RH, United Kingdom
Received for publication, September 6, 2000, and in revised form, October 24, 2000
 |
ABSTRACT |
C-H bond breakage by tryptophan
tryptophylquinone (TTQ)-dependent methylamine dehydrogenase
(MADH) occurs by vibrationally assisted tunneling (Basran, J.,
Sutcliffe, M. J., and Scrutton, N. S. (1999)
Biochemistry 38, 3218-3222). We show here a similar mechanism in TTQ-dependent aromatic amine dehydrogenase (AADH). The
rate of TTQ reduction by dopamine in AADH has a large, temperature independent kinetic isotope effect (KIE = 12.9 ± 0.2), which
is highly suggestive of vibrationally assisted tunneling. H-transfer is
compromised with benzylamine as substrate and the KIE is deflated (4.8 ± 0.2). The KIE is temperature-independent, but reaction rates are strongly dependent on temperature. With tryptamine as substrate reaction rates can be determined only at low temperature as
C-H bond cleavage is rapid, and an exceptionally large KIE (54.7 ± 1.0) is observed. Studies with deuterated tryptamine suggest vibrationally assisted tunneling is the mechanism of deuterium and, by
inference, hydrogen transfer. Bond cleavage by MADH using a slow
substrate (ethanolamine) occurs with an inflated KIE (14.7 ± 0.2 at 25 °C). The KIE is temperature-dependent, consistent with differential tunneling of protium and deuterium. Our observations illustrate the different modes of H-transfer in MADH and AADH with fast
and slow substrates and highlight the importance of barrier shape in
determining reaction rate.
 |
INTRODUCTION |
Aromatic amine dehydrogenase
(AADH)1 and methylamine
dehydrogenase (MADH) catalyze the oxidative deamination of primary
amines to their corresponding aldehydes and ammonia.
The physiological electron acceptors of MADH are amicyanin (for
the Paracoccus denitrificans enzyme; Refs. 1-3) or a
c-type cytochrome (for the Methylophilus
methylotrophus enzyme; Ref. 4). AADH transfers electrons (derived
from the deamination of aromatic amines) to the copper protein azurin
(5). In a reductive half-reaction, both enzymes reduce the prosthetic
group tryptophan tryptophylquinone (TTQ) through the initial formation of a carbinolamine intermediate (Fig. 1; Refs. 5 and 6); loss of water
from this carbinolamine produces an iminoquinone. The iminoquinone
decays by breakage of the substrate C-H bond. An active site base that
abstracts a proton from the substrate initiates bond cleavage (7). This
step in the reductive half-reaction is rate-limiting, as demonstrated
by the unusually large kinetic isotope effect (KIE) observed with
methylamine (MADH; Refs. 8-10) and dopamine (AADH; Ref. 11).
Previously we demonstrated that cleavage of the substrate C-H bond of
M. methylotrophus (sp. W3A1) MADH is
associated with a large KIE (16.8 ± 0.5) and that the KIE is
independent of temperature (8). Through detailed temperature dependence
studies, we were able to suggest that C-H bond breakage occurs by
extreme quantum tunneling (8). Quantum tunneling effects in enzymatic
hydrogen transfer have been observed in only a small number of enzyme
systems (8, 12-21). Most have been modeled using the classical
formulations of transition state theory, incorporating a tunneling
correction factor to account for tunneling below the saddle-point of
the potential energy surface. In our studies of H-tunneling in MADH, we
demonstrated that reaction rates were dependent on temperature, thus
providing experimental evidence suggesting a role for thermally induced, vibrational motion of the protein scaffold in driving enzymatic H-transfer (8). Recently, similar observations have been made
with a thermophilic alcohol dehydrogenase (22) and heterotetrameric
sarcosine oxidase (17). These observations point to the potential
general importance of protein dynamics in driving H-tunneling reactions
in enzymes (for recent reviews, see Refs. 23-26) and also to the
potential role of low frequency vibrations in facilitating catalysis
via the "over-the-barrier" route (27, 28).
In this paper we demonstrate that reduction of the TTQ cofactor by
dopamine in AADH also occurs by a vibrationally assisted tunneling
mechanism, thus establishing close similarities in the mode of bond
breakage with MADH and its physiological substrate, methylamine (8). We
also show that vibrationally assisted tunneling is the likely mechanism
of bond cleavage for the reaction of AADH with the slow substrate,
benzylamine. Compromised reaction rates with this substrate are
suggested to be a consequence of (i) increased width of the potential
energy barrier and (ii) a larger enthalpy of activation for deformation
of the protein structure to produce geometries compatible with
H-tunneling. By contrast, we also show that reactions of MADH with a
slow substrate (ethanolamine) require partial ascent of the potential
energy surface to facilitate the tunneling reaction, with D-tunneling
occurring higher up the potential energy barrier than H-tunneling.
Partial ascent of the barrier is required to reduce the tunneling
distance and thereby optimize the probability of transfer. These
studies highlight the different strategies used by enzymes to
facilitate H-transfer by quantum mechanical tunneling.
 |
EXPERIMENTAL PROCEDURES |
Enzymes and Substrates--
MADH was purified from M. methylotrophus (sp. W3A1) as described
previously (29). Following reoxidation of the purified enzyme with
100-fold excess ferricyanide, the enzyme was exchanged into 10 mM potassium phosphate buffer, pH 7.5, by gel exclusion chromatography. Enzyme concentration was determined using an extinction coefficient of 25,200 M
1
cm
1 at 440 nm for the oxidized enzyme (29).
AADH was purified from Alcaligenes faecalis IFO 14479 as
described (30). Following enzyme purification, AADH was exchanged into
10 mM BisTris-propane buffer, pH 7.5, by gel exclusion
chromatography. Enzyme concentration was determined using an extinction
coefficient of 27,600 M
1
cm
1 at 433 nm for the oxidized enzyme (30).
Deuterated dopamine HCl
((HO)2C6H3CH2CD2NH2
HCl, 94.4%), deuterated benzylamine HCl (C6D5CD2NH2 HCl,
99.6%), and deuterated tryptamine HCl
(tryptamine-
,
-d2HCl, 98%) were from CDN
Isotopes. Deuterated ethanolamine
(ethanol-1,1,2,2-d4-amine, 98%) was from CK Gas
Products Ltd. The chemical purity of the deuterated tryptamine,
ethanolamine, benzylamine, and dopamine was determined to be >99% by
either high performance liquid chromatography, NMR, or gas
chromatography, or a combination of these methods. The suppliers of
each of the deuterated compounds performed the analysis of chemical purity.
Stopped-flow Kinetic Studies--
Stopped-flow experiments were
performed using an Applied Photophysics SX.18MV stopped-flow
spectrophotometer. For single wavelength studies, data collected at 440 nm (MADH) and 456 nm (AADH) were analyzed using nonlinear least squares
regression analysis on an Acorn RISC PC using Spectrakinetics software
(Applied Photophysics). Experiments were performed by mixing MADH or
AADH contained in the desired buffer, with an equal volume of substrate
contained in the same buffer at the desired concentration. The
concentration of substrate was always at least 10-fold greater than
that of enzyme, thereby ensuring pseudo-first order reaction
conditions. For each substrate concentration, at least five replica
measurements were collected and averaged. The error for individual
rates measured by fitting to a single transient was, in all cases, less
than 0.5% of the determined value. Shot-by-shot variability in the determined rate was <5%, and the error for the rate fitted to averaged transients was <0.4% of the determined value. As reported previously for MADH (8) and AADH (5), the absorbance changes accompanying enzyme reduction were monophasic, with a single rate constant obtained from fits of the data to Equation 1.
|
(Eq. 1)
|
C is a constant related to the initial absorbance,
and b is an offset value to account for a nonzero base line.
Transients obtained for reactions of AADH with tryptamine were biphasic
and analyzed using a double exponential expression. The fast phase of
these transients (>90% of the total amplitude change) exhibited a
very large KIE (54.7 ± 1.0) and thus reflects C-H bond cleavage. The origin of the slow phase remains uncertain, but it may represent hydrolysis of the imine intermediate (intermediate 5; Fig. 1). The
small amplitude of the slow phase and studies using stopped-flow photodiode array spectroscopy clearly indicate that the slow phase is
not associated with TTQ reduction. The slow phase is not resolved in
reactions of AADH with deuterated tryptamine. The transients performed
with deuterated dopamine were fitted to Equation 1, but the very early
phase (0-30 ms) of the transient was omitted to avoid contamination of
the spectral change from any contribution from protiated substrate (the
deuterated dopamine was enriched to a minimal level of 94%). Due to
the large KIE with dopamine, analysis of the transient from around 30 ms onward using Equation 1 ensured that any spectral change
attributable to protiated data was in fact removed from the analysis,
while retaining virtually all of the kinetic transient for the
deuterated substrate. Although this precaution was taken in data
fitting, fits to the entire transient to a single exponential function
were excellent (with no obvious deviation in the early time domain) and
produced rates identical to those fits performed from 30 ms onwards.
These observations suggest that the level of enrichment of the
deuterated dopamine was greater than the minimal value (94%) quoted by
the supplier. For all substrates of MADH and AADH, the observed rate
constants were found to exhibit dependence on substrate concentration
and the reductive half-reactions of AADH and MADH were modeled using the following general scheme.
Data for MADH (ethanolamine as substrate) were fitted using the
simplified equation described by Hiromi (31) as described previously
for MADH with methylamine as substrate (8, 9).
|
(Eq. 2)
|
Data for AADH were fitted to the simpler equation (Equation 3;
Ref. 32), also as described previously for this enzyme (5).
|
(Eq. 3)
|
Here, K is a constant and equal to
(k2 + k3)/k1. For multiple
wavelength stopped-flow studies, the reaction was monitored using an
Applied Photophysics photodiode array detector and operated using XSCAN
software. For data analysis of photodiode array, we used PROKIN
software (Applied Photophysics). Both AADH and MADH are stable over the
temperature range used in the stopped-flow studies. This is evident
since the total absorption change for TTQ reduction at all temperatures
remains constant and is identical to that observed in
spectrophotometric titrations of the enzyme with its substrate. Enzymes
were equilibrated for 10 min in the stopped-flow apparatus at the
appropriate temperature prior to the acquisition of stopped-flow data.
The optimal time for equilibration was determined empirically.
Temperature control was achieved using a thermostatic circulating water
bath, and the temperature was monitored directly in the stopped-flow
apparatus using a semiconductor sensor (model LM35CZ, National
Semiconductor). In studies of the temperature dependence of bond
cleavage, all substrates were used at saturating concentrations.
Studies of the concentration dependence of bond cleavage at 5 °C and
35 °C indicated that the enzyme-substrate dissociation constant (for
MADH) and the value of K in Equation 3 (for AADH) were not
substantially perturbed on changing temperature. These control
experiments thus ensured that substrate was saturating at all the
temperatures investigated in the temperature dependence studies with
both MADH and AADH.
 |
RESULTS AND DISCUSSION |
Vibrationally Assisted H-tunneling in AADH--
AADH has a broad
specificity for primary amine substrates. Davidson and co-workers (5)
have investigated the substrate preference of AADH in steady-state
reactions and demonstrated that aromatic substrates are generally
preferred over simple aliphatic primary amines. Moreover, a large KIE
has been demonstrated with the aromatic substrate dopamine (11). In
this paper, we have extended the kinetic analysis with dopamine to
include studies of the effects of temperature on the KIE. We have also
probed the effects of temperature on the KIEs observed with
conventional and deuterated forms of benzylamine and tryptamine. The
dependence of [dopamine] on the rate of TTQ reduction in AADH is
illustrated in Fig. 2 for both deuterium- and protium-labeled
substrate. The data are similar to those reported previously with one
exception; the enzyme-substrate dissociation constant with dopamine in
the present study is much smaller (17.1 ± 0.8 µM)
than that reported previously (132 µM; Ref. 5). The
smaller dissociation constant for the Michaelis complex results from
the use of buffers of different ionic strength. Univalent cations are
known to elicit spectral changes in AADH, consistent with the presence
of a univalent cation-binding site in AADH (33). In the present work,
the [dopamine] dependence of TTQ reduction was performed at low ionic
strength (10 mM BisTris propane buffer, pH 7.5), whereas
previous studies were conducted at high ionic strength (0.25 M potassium phosphate buffer, pH 7.5; Ref. 5). The ionic
strength effects are limited to binding since the limiting rate of TTQ
reduction is similar in both the low and high ionic strength regimes.
The dependence of the TTQ reduction rate on [deuterated dopamine] is
also shown in Fig. 2. The term (k2 + k3)/k1 is larger with
dopamine (~17 µM) than with deuterated dopamine (~12
µM). Similar effects were seen with other substrates of
AADH (Figs. 3 and 4). The larger k3H
than k3D might account for this
observation with AADH (Equation 3). However, there might be an
additional contribution arising from the known differences in the
chemical nature of the C-H versus the C-D bond (34). This
is necessary to explain the difference in
k2/k1 (i.e. an
isotope effect on binding) for MADH obtained from fitting to Equation 2
(see Fig. 6 and previous work with methylamine (Ref. 8)). For example,
(i) the smaller effective bond length of C-D versus C-H
(the latter has a higher zero point energy and therefore lies higher in
the asymmetric potential energy well) results in a smaller effective
size of C-D relative to C-H; (ii) the shorter C-D bond results in a
larger charge density, and is therefore electron supplying relative to
C-H; and (iii) C-H has a higher dipole moment than C-D. The
expectation, therefore, is that the combined effects of multiple
isotopic substitution will perturb the dissociation of the
enzyme-substrate complex. These effects will likely be pronounced in
those cases where the isotopically substituted group is the main
determinant in formation of the enzyme-substrate complex (as is the
case with methylamine).
Fig. 2 reveals a large kinetic isotope effect for dopamine (12.9 ± 0.2) on TTQ reduction, indicating that, as with MADH, C-H bond
breakage is concerted with cofactor
reduction2 (Fig.
1). An indication as to whether
H-transfer occurs classically or by quantum tunneling can be gained by
investigating the temperature dependence of the rates of C-H and C-D
bond cleavage using the unimolecular rate Equation 4 (8).
|
(Eq. 4)
|
kB and h are the Boltzmann and
Planck constants, respectively. Temperature-dependent rate
data can be plotted conveniently using the following form of the Eyring
equation.
|
(Eq. 5)
|
The enthalpy of activation
H
is
calculated from the slope of the plot,
S
is calculated by extrapolation to the ordinate axis, and
G
is then calculated directly from
Equation 4. As discussed previously (8), the use of Equation 5 in
plotting the temperature dependence of a unimolecular reaction is
preferred over the use of the classical Arrhenius plot. This arises
because the Arrhenius equation is in fact curved (although it
appears linear in the accessible temperature range) and asymptotically
approaches infinity at high temperatures. A consequence of using
Equation 5 is the need to define explicitly the meaning of values
obtained from such plots. Use of the Arrhenius plot has led to the
development of criteria to indicate tunneling based on the values for

Ea and the
AH:AD ratio (calculated
from the intercepts of the Arrhenius plot for protium and deuterium
substrates). The corresponding parameters calculated from the slopes
and intercepts of plots using Equation 5 are

H
and
A'H:A'D (the prime is
used to distinguish this ratio from the
AH:AD ratio calculated
from the Arrhenius plot).

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Fig. 1.
Reaction mechanism for the reductive
half-reaction of MADH. Steps enclosed in the hatched
box represent binding steps: rate constants
k1 (forward reaction) and
k2 (reverse reaction). A similar scheme has been
proposed for the reaction of AADH with aromatic primary amines.
|
|
Analysis of the temperature dependence of k3
using Equation 5 is illustrated in Fig.
2. The data indicate that the KIE is independent of temperature and that the difference in the enthalpy of
activation for protium versus deuterium transfer
(
H
=
H
D
H
H = 0.7 ± 1.5 kJ
mol
1) is essentially zero. The value of the
A'H:A'D ratio (9.4 ± 1.6) calculated from the intercepts of the plots is similar to that
of the KIE (12.8 ± 0.2), indicating that the reaction proceeds
predominantly by quantum tunneling. Observations similar to those
discussed above for the temperature-dependent behavior of
C-H bond breakage in AADH have been made during cleavage of a
substrate C-H bond by the TTQ-dependent methylamine
dehydrogenase (MADH) of M. methylotrophus. For MADH the data
were interpreted in terms of vibrationally assisted tunneling of
protium and deuterium through a fluctuating potential energy barrier
(8). Our data for the reaction catalyzed by AADH indicate that this
mechanistically similar enzyme catalyzes H-transfer by ground state
tunneling of protium and deuterium and that tunneling is driven by the
thermal motion.

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Fig. 2.
Stopped-flow kinetic data for the reaction of
AADH with dopamine and deuterated dopamine. Panel
A, plot of observed rate constant
(kobs) against dopamine concentration for the
reduction of the TTQ cofactor in AADH. Reactions were performed in 10 mM BisTris propane buffer, pH 7.5, at 25 °C. Transients
were measured at 456 nm; [AADH] 1.3 µM. The fits shown
are to the standard hyperbolic expression (Equation 3).
Closed circles, dopamine; open
circles, deuterated dopamine
((HO)2C6H3CH2CD2NH2).
For dopamine fitted to Equation 3, k3 = 132 ± 1 s 1, Kd = 17.1 ± 0.8 µM. For deuterated dopamine fitted to Equation 3,
k3 = 10.3 ± 0.1 s 1, Kd = 12.1 ± 0.6 µM. Panel B, temperature dependence
and KIE data for the reaction of AADH with dopamine. Main
panel, temperature dependence plots for AADH with dopamine
(closed circles) and deuterated dopamine
(open circles).
ln(A'H) = 19.7 ± 0.3, ln(A'D) = 17.5 ± 0.3, H (C-H) = 50.9 ± 0.7 kJ
mol 1, H (C-D) = 51.6 ± 0.7 kJ mol 1. Inset,
plot of ln(KIE) versus 1/T. Rate constants are
observed rate constants measured at 500 µM
dopamine.
|
|
The KIE data with dopamine indicate that H-transfer is not by the
classical, over-the-barrier route and that quantum tunneling is the
mechanism of transfer. Moreover, the data are inconsistent with rigid
barrier models of H-tunneling since the vibrational assistance (as
indicated by the nature of the temperature dependence plots) requires a
fluctuating potential energy barrier for the transfer event.
Vibrational assistance has been discussed for many years with regard to
classical over-the-barrier reactions (35), but only relatively recently
has this been applied to enzymatic quantum tunneling reactions.
Temperature-independent KIEs with large enthalpies of activation can be
interpreted in a number of ways. The dynamic component may reflect
substrate vibrations, protein vibrations, or a combination of the two.
Both Antoniou and Schwartz (36) and Borgis and Hynes (37) have provided
theoretical descriptions of H-tunneling facilitated by vibrations in
the substrate. Alternatively, Bruno and Bialek (38) have proposed that
H-tunneling is facilitated by vibrations in the protein, and they have
derived a relationship between the intrinsic KIE for C-H bond cleavage
and temperature for tunneling reactions occurring from the vibrational
ground state of the substrate. Importantly, in this treatment the KIE
can adopt values below the "semiclassical" limit of 7 (at
25 °C); values in this limit and in systems consistent with
tunnelling have recently been obtained experimentally for some enzymes
(17, 22). A more general treatment of enzymatic H-tunneling involving
coupling between the tunneling modes and the environment and a
fluctuating barrier has been described recently by Kuznetsov and
Ulstrop (39). Although we acknowledge that the degree and nature of
H-tunneling in enzymatic systems is model-dependent, we
feel our data are most consistent with the model proposed by Bruno and
Bialek. In particular, the lack of an isotope effect on the activation
enthalpy for H- and D-transfer suggests to us that normal vibrational
modes of the substrate alone are not the major component of the
vibrational assistance observed with AADH. We envisage this vibrational
assistance comes predominantly from vibrational modes in the enzyme.
Reaction of AADH with Tryptamine and Benzylamine--
The very
fast rates of C-H bond cleavage catalyzed by AADH with tryptamine as
substrate prevented detailed studies of the dependence of the reaction
rate on temperature. Studies of the dependence of the rate of TTQ
reduction on [tryptamine] at 4 °C revealed a highly inflated KIE
(54.7 ± 1.0) for bond cleavage (Fig.
3, panel A). This
highly inflated KIE is not the result of inhibitory components in the
deuterated tryptamine sample. Reference to Fig. 3A indicates
that, at low tryptamine concentrations (5 µM), there is
still a sizeable KIE. At this concentration of substrate, the maximum
concentration of a potential inhibitor would be <0.05 µM
(based on >99% purity of the sample) and the AADH concentration is
1.3 µM. Clearly, therefore, reactions of AADH with
potential inhibitor would be much less than stoichiometric. Additionally, the concentration dependence data for reactions with
deuterated tryptamine fit well to the standard hyperbolic expression.
If inhibitors were present, one might expect the hyperbolic dependence
to break down at low substrate concentrations, as any potential
inhibitor is effectively diluted out. Moreover, transients obtained
with a 50:50 mixture of tryptamine and deuterated tryptamine (35 µM each) have a tangent at time 0 equal to the average of the tangents obtained with tryptamine (70 µM) and
deuterated tryptamine (70 µM) alone. This observation
again argues for the lack of an inhibitory component in deuterated
tryptamine. Due to the large KIE, studies of the dependence of reaction
rates on temperature were possible using deuterated tryptamine (Fig. 3,
panel B). Studies with deuterated substrate
revealed that
H
Dtryptamine =
H
Ddopamine =
H
Hdopamine (Table
I). Even though detailed studies of the
variation in reaction rate with temperature were not possible with
tryptamine, our investigations with deuterated tryptamine suggest that
vibrationally assisted tunneling (probably from the vibrational ground
state of the substrate in accordance with the model of Bruno and
Bialek) is the mechanism of H-transfer with this substrate. This
follows, since either tunneling from an excited state or transfer
over-the-barrier would likely manifest itself as
H
Dtryptamine >
H
Ddopamine. Comparable studies
were also performed using the slow substrate benzylamine (Fig.
4, panels A and
B). In this case, the KIE (4.8 ± 0.2) is reduced
compared with dopamine (KIE = 12.9 ± 0.2) and tryptamine
(KIE = 54.7 ± 1.0), but temperature dependence studies
suggest that vibrationally assisted tunneling occurs from the
vibrational ground state of the substrate. In particular, the
temperature dependence plots (Fig. 4, panel B) illustrate the parallel nature of the C-H and C-D data
(
H
Hbenzylamine =
H
Dbenzylamine), and the
A'H:A'D ratio is
comparable with the KIE (Table I; indicating that the reaction proceeds
predominantly by quantum tunneling). With benzylamine, however, the
enthalpy of activation is higher than that seen with dopamine and
tryptamine. The data thus suggest that there is a larger energetic cost
in deforming the enzyme-substrate iminoquinone intermediate with this
substrate, which is required to facilitate H-tunneling by barrier
compression and equalization of the reactant and product energies.

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Fig. 3.
Stopped-flow kinetic data for the reaction of
AADH with tryptamine and deuterated tryptamine. Panel
A, plot of observed rate constant
(kobs) against [tryptamine] and [deuterated
tryptamine]. Reactions were performed in 10 mM BisTris
propane buffer, pH 7.5, at 4 °C. Transients were measured at 456 nm;
[AADH] 1.3 µM. The fits shown are to the standard
hyperbolic expression (Equation 3). Closed
circles, tryptamine; open circles,
deuterated tryptamine
(tryptamine- , -d2HCl). For tryptamine
fitted to Equation 3, k3 = 503 ± 5 s 1, Kd = 4.5 ± 0.3 µM. For deuterated tryptamine fitted to Equation 3,
k3 = 9.25 ± 0.07 s 1, Kd < 4 µM (value is too small to measure using the stopped-flow
technique). Panel B, temperature dependence plot
for reaction of AADH with deuterated tryptamine.
ln(A'D) = 19.8 ± 0.5, H (C-D) = 53.5 ± 1.2 kJ
mol 1. Rate constants are observed rate
constants measured at 180 µM deuterated tryptamine.
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Table I
Kinetic isotope effects and activation parameters for reactions of AADH
and MADH with primary amine substrates
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Fig. 4.
Stopped-flow kinetic data for the reaction of
AADH with benzylamine and deuterated benzylamine. Panel
A, plot of observed rate constant
(kobs) against [benzylamine] and [deuterated
benzylamine]. Reactions were performed in 10 mM BisTris
propane buffer, pH 7.5, at 25 °C. Transients were measured at 456 nm; [AADH] 1.3 µM. The fits shown are to the standard
hyperbolic expression (Equation 3). Closed
circles, benzylamine; open circles,
deuterated benzylamine
[C6D5CD2NH2 HCl]. For
benzylamine fitted to Equation 3, k3 = 1.81 ± 0.02 s 1, Kd = 7.4 ± 0.5 µM. For deuterated benzylamine fitted to Equation 3, k3 = 0.38 ± 0.01 s 1, Kd = 6.8 ± 0.7 µM. Panel B, temperature dependence
plots for AADH with benzylamine (closed circles)
and deuterated benzylamine (open circles).
ln(A'H) = 21.8 ± 0.4, ln(A'D) = 20.6 ± 0.6, H (C-H) = 68.1 ± 1.4 kJ
mol 1, H (C-D) = 67.1 ± 0.9 kJ mol 1. Inset,
plot of ln(KIE) versus 1/T. Rate constants are
observed rate constants measured at 200 µM
benzylamine.
|
|
Variation in KIE as a Function of Barrier Width--
Our studies
with AADH suggest that the cleavage of the substrate C-H bond with
slow (benzylamine) and fast (dopamine and tryptamine) substrates occurs
by a vibrationally assisted tunneling mechanism. This tunneling process
is consistent with KIE values ranging from 4.8 (benzylamine) to 54.7 (tryptamine), and an explanation for this variation in KIE needs to be sought.
Considering the effect of barrier width (and shape) on wave function
decay for the protium and deuterium nuclei, one can develop an
explanation for the variation in intrinsic KIE with different substrates. Effects of barrier shape on quantum tunneling reactions have been discussed previously (e.g. Ref. 40). These
analyses have invoked static potential energy barriers and discussed
idealized barrier shapes (e.g. truncated parabolic).
Although a fluctuating potential energy barrier is consistent with our
experimental observations, we have discussed previously (8, 23, 24)
that the tunneling event can be visualized as a two-step process. The
first step is dynamical in nature and is required to activate the
enzyme-substrate complex by thermal vibration. In essence, it leads to
a crossing over of the potential energy surfaces for the
enzyme-substrate and enzyme-product complexes. The second step is a
quantum tunneling component, which occurs only when the activated
complex is populated (i.e. at the crossing point of the
enzyme-substrate and enzyme-product potential energy curves). Thus,
although we have established experimentally that the potential energy
barrier to the reaction is fluctuating, when the geometry is compatible
with quantum tunneling (i.e. at intersection point of the
potential energy surfaces of the enzyme-substrate and enzyme-product
complexes), the tunneling barrier can be treated as being rigid for the
lifetime of the tunneling event. In the discussion below, therefore, we
have used rigid barrier depictions of H-tunneling to predict the effect
of barrier shape and width on the value of the KIE obtained.
Factors that enhance tunneling are a small particle mass (increased de
Broglie wavelength) and a small area under the potential energy
barrier, but the barrier needs to be sufficiently high to favor
tunneling, rather than classical over-the barrier, reactions; thus,
high, narrow barriers are particularly favorable for efficient tunneling. In the simplest cases, the rate of reaction, k,
is proportional to the probability of passing through a classically forbidden barrier, Ptunnel, which is given by
Equation 6 (41).
|
(Eq. 6)
|
In Equation 6, S is known as the
Wentzel-Kramers-Brillouin action, V(x) is the
potential energy barrier, and E is the zero point energy of
the H nucleus.
To illustrate the effect of H- versus D-tunneling,
consider first the simplest potential energy barrier: a
rectangular barrier (height V, width
l; Fig. 5, panel
A; the possible role of a rectangular barrier in
vibrationally assisted tunneling has been discussed in detail
previously in Ref. 38). The amplitude of the wave function (kinetic
energy E) decreases exponentially within the barrier, and
the tunneling rate, k, is related to the mass of the
tunneling particle, m, by the following relationship.
|
(Eq. 7)
|
Inspection of Equation 7 reveals that, for a nucleus of a given
mass, k decays exponentially with increased tunneling
distance and/or increased barrier height. Thus, given the observed
rates (Table I), a rectangular barrier predicts that tunneling from tryptamine occurs over a shorter distance and/or through a lower barrier than tunneling from dopamine, which in turn occurs over a
shorter distance and/or through a lower barrier than tunneling from
benzylamine. The KIE can be obtained from Equation 7 as follows.
|
(Eq. 8)
|
In Equation 8, kD and
kH, mD and
mH, and ED and
EH are the tunneling rates for, masses, and zero
point energies of D and H, respectively. Equation 8 reveals that the
KIE increases exponentially with the tunneling distance
and/or barrier height. Thus, for the observed KIEs (Table I), a
rectangular barrier predicts that tunneling from tryptamine occurs over
a longer distance and/or through a higher barrier
than tunneling from dopamine, which in turn occurs over a
longer distance and/or through a higher barrier than from benzylamine. This discrepancy between the relative tunneling distances and/or barrier heights derived from k and KIE
values (Fig. 5, panel C) clearly illustrates that
the rectangular barrier is not the correct shape for the reaction of
AADH with the substrates tryptamine, dopamine, and benzylamine.

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Fig. 5.
Tunneling through a variety of potential
energy barriers. A, tunneling of wave function, ,
kinetic energy E, through a rectangular potential energy
barrier, height V. The narrower the barrier, the smaller the
mass of the particle and the smaller V, the greater the
tunneling probability. If the amplitude of has not reached 0 at the
far side of the barrier, it will stop decaying and resume the
oscillation it had on entering the barrier (but with smaller
amplitude). B, tunneling of wave function, , kinetic
energy E, through a truncated parabola potential energy
barrier total height V, maximum width 2a,
tunneling distance 2l. C, schematic representation of
tryptamine, dopamine, and benzylamine tunneling through a rectangular
barrier. The experimental rates (kT,
kD, and kB for
tryptamine, dopamine, and benzylamine, respectively; additional
subscripts H and D denote protium and deuterium,
respectively) suggest increased tunneling distance and/or increased
barrier height in passing from tryptamine to dopamine to benzylamine.
However, this is inconsistent with the observed KIEs. D,
schematic representation of tryptamine, dopamine, and benzylamine
tunneling through a truncated parabolic barrier. The experimental rates
suggest increased tunneling distance and/or increased barrier height in
passing from tryptamine to dopamine to benzylamine. However, this is
inconsistent with the observed KIEs. E, a possible barrier
shape that is consistent with the trend in both the experimentally
observed rates and the experimentally observed KIEs. In this barrier,
it is the narrowest part of the barrier, rather than the whole barrier,
that becomes progressively wider. This results in the concave shoulder
becoming less pronounced.
|
|
A truncated parabolic potential energy barrier provides an
alternative barrier shape (40) (Fig. 5, panel B). The potential, V(x), can be described by Equation 9.
|
(Eq. 9)
|
V is the height of the barrier and 2a is the
maximum width of the barrier. The tunneling rate, k, is
related to the mass of the tunneling particle, m, and the
tunneling distance, 2l, by the following relationship.
|
(Eq. 10)
|
l can be removed from Equation 10, thus making
interpretation easier, by using Equation 9 to write l in
terms a, V, and E (the zero point
energy).
|
(Eq. 11)
|
Substituting Equation 11 in Equation 10 gives Equation 12.
|
(Eq. 12)
|
As with the rectangular barrier, given the observed rates (Table
I), a truncated parabolic barrier predicts that tunneling from
tryptamine occurs through a narrower barrier than tunneling from
dopamine, which in turn occurs through a narrower barrier than
tunneling from benzylamine. Additionally, it can be shown numerically
from Equation 12 that, for a fixed barrier width (i.e. fixed
value of a), the barrier height must increase from
tryptamine to dopamine to benzylamine to explain the trend in the
experimental rates. The KIE can be obtained from Equation 12,
giving Equation 13.
|
(Eq. 13)
|
As with the rectangular barrier, Equation 13 reveals that, for a
truncated parabolic barrier, the KIE increases exponentially with the barrier width, thus predicting that tunneling from tryptamine occurs over a longer distance than tunneling from dopamine,
which in turn occurs over a longer distance than from
benzylamine. Additionally, it can be shown numerically from Equation 13
that, for a fixed barrier width, increasing the barrier height
increases the predicted KIE. Again, this discrepancy between
the relative tunneling distances and/or barrier heights derived from
k and KIE values (Fig. 5, panel D)
clearly illustrates that the truncated parabolic barrier is not the
correct shape for the reaction of AADH with the substrates tryptamine,
dopamine, and benzylamine.
Rectangular and parabolic barriers are appropriate (albeit crude)
depictions of the potential energy surface near the top of the barrier.
Other barrier shapes have been suggested, e.g. Eckart and Gaussian (40). It could be argued that
Eckart and Gaussian (along with other shapes) barriers are more
realistic depictions of the potential energy surface when tunneling is
from the vibrational ground state of the substrate. However, our
experimental data suggest that a "nonstandard" barrier shape may be
required to explain the experimental observations. One possible shape
that is consistent with the trends in experimental rates and KIEs is shown in Fig. 5 (panel E; note that, in this
schematic, for simplicity we have assumed that it is only the barrier
width that changes, and not the height, although in practice both will
likely vary). The advantage of this barrier over those discussed above
is that it has a concave shoulder occurring just below where H tunnels, which provides a possible explanation for the relatively high rates and
high KIE observed for tryptamine. The relatively fast rates for
tryptamine can be explained by tunneling occurring through a relatively
narrow barrier compared with dopamine and benzylamine. The large KIE
for tryptamine can be explained by D tunneling through a shoulder below
the narrow part of the barrier, whereas H tunnels above this shoulder
through the narrow part of the barrier; thus, D would tunnel
significantly further than H. The narrowest part of the barrier is
positioned closer to the reactants than to the products, as this part
of the potential energy surface is likely to correspond to the point at
which the C-H and C-D bonds are broken. As the enzyme-catalyzed
reaction becomes less efficient, one possible scenario is that the
narrowest part of the barrier could become progressively broader and,
as a result, the shoulder become increasingly less pronounced. Thus,
with dopamine (Fig. 5, panel E), the shoulder
could still be present but H, and to a much lesser extent D, would have
further to tunnel than with tryptamine. This would manifest itself in
(i) slower rates and (ii) a lower KIE for dopamine than tryptamine.
With benzylamine, the shoulder could be less pronounced still. Thus,
although the integrated area under the barrier has become larger and
this would be expected to result in higher KIEs, this is more than
offset by the more similar tunneling distances for H and D and
manifests itself in (i) the slowest rates and (ii) the lowest KIE of
the three AADH substrates.
Although the barrier shape depicted in Fig. 5 (panel
E) is consistent with experimental data, it is nevertheless
just one possibility; the true nature of the barrier shape for AADH
(and MADH) remains to be established. These barriers are currently being investigated using quantum mechanical/molecular mechanical computational methods.
Reaction of MADH with the Slow Substrate Ethanolamine--
We have
also probed the effect of using slow substrates on the quantum
tunneling reaction catalyzed by MADH. The dependence of the rate of TTQ
reduction on [ethanolamine] is shown in Fig. 6 and the associated parameters in Table
I. The limiting rates of TTQ reduction are approximately 1 order of
magnitude slower than those observed with methylamine (Table I).
Temperature dependence studies of TTQ reduction with ethanolamine (Fig.
6; Table I) indicate that the mechanism of slow substrate oxidation by
MADH is different to that of AADH. With AADH, temperature-independent KIEs were observed with dopamine and benzylamine. In reactions of MADH
with ethanolamine, however, the KIE is
temperature-dependent,
H
Dethanolamine >
H
Hethanolamine and
A'H:A'D < 1. These
parameters suggest that tunneling does occur with ethanolamine, but
that tunneling with the deuterated substrate is from part way up the
potential energy barrier (42). Partial ascent of the barrier with
deuterated substrate by thermal activation will reduce the barrier
width to the point where nuclear tunneling becomes favorable. The extra
thermal energy required for this process is reflected in the relatively
large value of
H
Dethanolamine
compared with
H
Hethanolamine.
In all likelihood, protium transfer from ethanolamine to MADH is from
the ground state since
H
Hethanolamine =
H
Hmethylamine (Table I). The
decrease in rate observed with ethanolamine is likely due to an
increase in barrier width/height.

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Fig. 6.
Stopped-flow kinetic data for the reaction of
MADH with ethanolamine and deuterated ethanolamine.
Panel A, plot of observed rate constant
(kobs) against [ethanolamine] and [deuterated
ethanolamine]. Reactions were performed in 10 mM Bis
potassium phosphate buffer, pH 7.5, at 25 °C. Transients were
measured at 440 nm; [MADH] 1.3 µM. The fits shown are
to the standard hyperbolic expression (Equation 3). Closed
circles, ethanolamine; open circles,
deuterated ethanolamine
(ethanol-1,1,2,2-d4-amine). For ethanolamine
fitted to Equation 3, k3 = 14.1 ± 0.07 s 1, Kd = 171 ± 4 µM. For deuterated ethanolamine fitted to Equation 3,
k3 = 0.96 ± 0.01 s 1, Kd = 175 ± 11 µM. Panel B, temperature dependence
plots for MADH with ethanolamine (closed circles)
and deuterated ethanolamine (open circles).
ln(A'H) = 20.2 ± 0.2, ln(A'D) = 20.7 ± 0.4, H (C-H) = 43.5 ± 0.6 kJ
mol 1, H (C-D) = 51.9 ± 1.1 kJ mol 1. Inset,
plot of ln(KIE) versus 1/T. Rate constants are
observed rate constants measured at 4 mM
ethanolamine.
|
|
Conclusions--
TTQ-dependent amine dehydrogenases
catalyze C-H bond cleavage by a vibrationally assisted quantum
tunneling mechanism. We infer that the size of the KIE with alternative
substrates varies with barrier width, as expected for a pure tunneling
reaction. Experimental data are inconsistent with idealized rectangular and truncated parabolic energy barriers, but are consistent with more
complex barrier shapes for C-H bond cleavage. Deuterium transfer from
a slow substrate (ethanolamine) to MADH requires partial ascent of the
potential energy surface to reduce the tunneling pathway distance.
 |
FOOTNOTES |
*
This work was funded by grants from the Biotechnology and
Biological Sciences Research Council and the Lister Institute of Preventive Medicine.The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement" in
accordance with 18 U.S.C. Section
1734 solely to indicate this fact.
§
These authors contributed equally to this work.
A Lister Institute research professor. To whom
correspondence should be addressed. Tel.: 44-116-223-1337; Fax:
44-116-252-3369; E-mail, nss4@le.ac.uk.
Published, JBC Papers in Press, November 21, 2000, DOI 10.1074/jbc.M008141200
2
Although secondary KIEs can make significant
contributions to observed KIEs, and therefore affect their
interpretation, they should not compromise the analysis in this case. A
predicted upper value for the secondary KIE is 1.15 for
reactions involving a change in hybridization
(sp3 to sp2) (43), which
represents ~8% of the observed KIE.
 |
ABBREVIATIONS |
The abbreviations used are:
AADH, aromatic amine
dehydrogenase;
MADH, methylamine dehydrogenase;
KIE, kinetic isotope
effect;
TTQ, tryptophan tryptophylquinone;
BisTris, bis(2-hydroxyethyl)iminotris (hydroxymethyl)methane.
 |
REFERENCES |
1.
|
Chen, L. Y.,
Durley, R.,
Poliks, B. J.,
Hamada, K.,
Chen, Z. W.,
Mathews, F. S.,
Davidson, V. L.,
Satow, Y.,
Huizinga, E.,
Vellieux, F. M. D.,
and Hol, W. G. J.
(1992)
Biochemistry
31,
4959-4964[Medline]
[Order article via Infotrieve]
|
2.
|
Chen, L. Y.,
Durley, R. C. E.,
Mathews, F. S.,
and Davidson, V. L.
(1994)
Science
264,
86-90[Medline]
[Order article via Infotrieve]
|
3.
|
Brooks, H. B.,
and Davidson, V. L.
(1994)
Biochemistry
33,
5696-5701[Medline]
[Order article via Infotrieve]
|
4.
|
Chandrasekar, R.,
and Klapper, M. H.
(1986)
J. Biol. Chem.
261,
3616-3619[Abstract/Free Full Text]
|
5.
|
Hyun, Y.-L.,
and Davidson, V. L.
(1995)
Biochemistry
34,
12249-12254[Medline]
[Order article via Infotrieve]
|
6.
|
Davidson, V. L.,
Jones, L. H.,
and Graichen, M. E.
(1992)
Biochemistry
31,
3385-3390[Medline]
[Order article via Infotrieve]
|
7.
|
Chen, L. Y.,
Mathews, F. S.,
Davidson, V. L.,
Huizinga, E. G.,
Vellieux, F. M. D.,
and Hol, W. G. J.
(1992)
Proteins Struct. Funct. Genet.
14,
288-299[Medline]
[Order article via Infotrieve]
|
8.
|
Basran, J.,
Sutcliffe, M. J.,
and Scrutton, N. S.
(1999)
Biochemistry
38,
3218-3222[CrossRef][Medline]
[Order article via Infotrieve]
|
9.
|
Brooks, H. B.,
Jones, L. H.,
and Davidson, V. L.
(1993)
Biochemistry
32,
2725-2729[Medline]
[Order article via Infotrieve]
|
10.
|
McWhirter, R. B.,
and Klapper, M. H.
(1989)
in
PQQ and Quinoproteins
(Jongejan, J. A.
, and Duine, J. A., eds)
, p. 259, Kluwer Academic Publishers, Dordrecht, The Netherlands
|
11.
|
Hyun, Y. L.,
and Davidson, V. L.
(1995)
Biochim. Biophys. Acta
1251,
198-200[Medline]
[Order article via Infotrieve]
|
12.
|
Cha, Y.,
Murray, C. J.,
and Klinman, J. P.
(1989)
Science
243,
1325-1330[Medline]
[Order article via Infotrieve]
|
13.
|
Grant, K. L.,
and Klinman, J. P.
(1989)
Biochemistry
28,
6597-6605[Medline]
[Order article via Infotrieve]
|
14.
|
Jonsson, T.,
Edmondson, D. E.,
and Klinman, J. P.
(1994)
Biochemistry
33,
14871-14878[Medline]
[Order article via Infotrieve]
|
15.
|
Jonsson, T.,
Glickman, M. H.,
Sun, S.,
and Klinman, J. P.
(1996)
J. Am. Chem. Soc.
118,
10319-10320[CrossRef]
|
16.
|
Kohen, A.,
Jonsson, T.,
and Klinman, J. P.
(1997)
Biochemistry
36,
2603-2611[CrossRef][Medline]
[Order article via Infotrieve]
|
17.
|
Harris, R. J.,
Meskys, R.,
Sutcliffe, M. J.,
and Scrutton, N. S.
(2000)
Biochemistry
39,
1189-1198[CrossRef][Medline]
[Order article via Infotrieve]
|
18.
|
Alston, W. C., II,
Kanska, M.,
and Murray, C. J.
(1996)
Biochemistry
35,
12873-12881[CrossRef][Medline]
[Order article via Infotrieve]
|
19.
|
Karsten, W. E.,
Hwang, C. C.,
and Cook, P. F.
(1999)
Biochemistry
38,
4398-4402[CrossRef][Medline]
[Order article via Infotrieve]
|
20.
|
Whittaker, M. M.,
Ballou, D. P.,
and Whittaker, J. W.
(1998)
Biochemistry
37,
8426-8436[CrossRef][Medline]
[Order article via Infotrieve]
|
21.
|
Nesheim, J. C.,
and Lipscomb, J. D.
(1996)
Biochemistry
35,
10240-10247[CrossRef][Medline]
[Order article via Infotrieve]
|
22.
|
Kohen, A.,
Cannio, R.,
Bartolucci, S.,
and Klinman, J. P.
(1999)
Nature
399,
496-499[CrossRef][Medline]
[Order article via Infotrieve]
|
23.
|
Sutcliffe, M. J.,
and Scrutton, N. S.
(2000)
Phil. Trans. R. Soc. Ser. A
358,
367-386[CrossRef]
|
24.
|
Scrutton, N. S.,
Basran, J.,
and Sutcliffe, M. J.
(1999)
Eur. J. Biochem.
264,
666-671[Abstract/Free Full Text]
|
25.
|
Kohen, A.,
and Klinman, J. P.
(1999)
Chem. Biol.
6,
R191-R198[CrossRef][Medline]
[Order article via Infotrieve]
|
26.
|
Sutcliffe, M. J.,
and Scrutton, N. S.
(2000)
Trends Biochem. Sci
25,
405-408[CrossRef][Medline]
[Order article via Infotrieve]
|
27.
|
Cannon, W. R.,
Singleton, S. F.,
and Benkovic, S. J.
(1996)
Nat. Struct. Biol.
3,
821-833[Medline]
[Order article via Infotrieve]
|
28.
|
Bruice, T.,
and Benkovic, S.
(2000)
Biochemistry
39,
6267-6274[CrossRef][Medline]
[Order article via Infotrieve]
|
29.
|
Davidson, V. L.
(1990)
Methods Enzymol.
188,
241-246[Medline]
[Order article via Infotrieve]
|
30.
|
Govindaraj, S.,
Eisenstein, E.,
Jones, L. H.,
Sanders-Loehr, J.,
Chistoserdov, A. Y.,
Davidson, V. L.,
and Edwards, S. L.
(1994)
J. Bacteriol.
176,
2922-2929[Abstract]
|
31.
|
Hiromi, K.
(1979)
Kinetics of Fast Enzyme Reactions
, Halsted Press, New York
|
32.
|
Strickland, S.,
Palmer, G.,
and Massey, V.
(1975)
J. Biol. Chem.
250,
4048-4052[Medline]
[Order article via Infotrieve]
|
33.
|
Zhu, Z.,
and Davidson, V. L.
(1998)
Biochem. J.
329,
175-182[Medline]
[Order article via Infotrieve]
|
34.
|
Van Hook, W. A.
(1971)
in
Isotope Effects in Chemical Reactions
(Collins, C. J.
, and Bowman, N. S., eds)
, pp. 1-89, van Nostrand Reinhold, New York
|
35.
|
Kramers, H. A.
(1940)
Physica (Utrecht)
7,
284-304
|
36.
|
Antoniou, D.,
and Schwartz, S. D.
(1997)
Proc. Natl. Acad. Sci. U. S. A.
94,
12360-12365[Abstract/Free Full Text]
|
37.
|
Borgis, D.,
and Hynes, J. T.
(1991)
J. Chem. Phys.
94,
3619-3628[CrossRef]
|
38.
|
Bruno, W. J.,
and Bialek, W.
(1992)
Biophys. J.
63,
689-699[Abstract]
|
39.
|
Kuznetsov, A. M.,
and Ulstrup, J.
(1999)
Can. J. Chem.
77,
1085-1096[CrossRef]
|
40.
|
Brunton, G.,
Griller, D.,
Barclay, L. R. C.,
and Ingold, K. U.
(1976)
J. Am. Chem. Soc.
98,
6803-6811
|
41.
|
Miller, W. H.
(1986)
Science
233,
171-177
|
42.
|
Bell, R. P.
(1980)
The Tunnel Effect in Chemistry
, pp. 51-140, Chapman and Hall, London
|
43.
|
Klinman, J. P.
(1978)
Adv. Enzymol. Relat. Areas Mol. Biol.
46,
415-494[Medline]
[Order article via Infotrieve]
|
Copyright © 2001 by The American Society for Biochemistry and Molecular Biology, Inc.