Differential quantum tunneling contributions in
nitroalkane oxidase catalyzed and the uncatalyzed
proton transfer reaction
Dan T. Major,a,b,1Annie Heroux,cAllen M. Orville,c,1Michael P. Valley,dPaul F. Fitzpatrick,d,1and Jiali Gaoa,1
aDepartment of Chemistry, Supercomputing Institute and Digital Technology Center, University of Minnesota, Minneapolis, MN 55455;bDepartment of
Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel;cDepartment of
Biology, Brookhaven National Laboratory, Upton, NY 11973; anddDepartment of Biochemistry, University of Texas Health Science Center at San Antonio,
San Antonio, TX 78229
Communicated by Vern L. Schramm, Albert Einstein College of Medicine, Bronx, NY, October 6, 2009 (received for review July 27, 2009)
The proton transfer reaction between the substrate nitroethane
and Asp-402 catalyzed by nitroalkane oxidase and the uncatalyzed
process in water have been investigated using a path-integral
free-energy perturbation method. Although the dominating effect
in rate acceleration by the enzyme is the lowering of the quasi-
classical free energy barrier, nuclear quantum effects also contrib-
ute to catalysis in nitroalkane oxidase. In particular, the overall
nuclear quantum effects have greater contributions to lowering
the classical barrier in the enzyme, and there is a larger difference
in quantum effects between proton and deuteron transfer for the
enzymatic reaction than that in water. Both experiment and
computation show that primary KIEs are enhanced in the enzyme,
and the computed Swain-Schaad exponent for the enzymatic
reaction is exacerbated relative to that in the absence of the
enzyme. In addition, the computed tunneling transmission coeffi-
cient is approximately three times greater for the enzyme reaction
be attributed to a narrowing effect in the effective potentials for
tunneling in the enzyme than that in aqueous solution.
PI-FEP/UM simulations ? enzyme catalysis ? kinetic isotope effects ?
enzymatic reaction in comparison with the uncatalyzed process
(1–3), quantum mechanical tunneling has been recognized to
also play a role in enzymatic hydrogen transfer reactions (2, 3).
An intriguing, yet unanswered, question is whether enzymes
because quantum effects on rate acceleration are much smaller
than hydrogen bonding and electrostatic stabilization of the
transition state (1, 4, 5). Nevertheless, a small factor of two in
rate enhancement can have important physiological impacts.
Although it appears straightforward to address this question by
comparing the enzymatic and the uncatalyzed reaction in solu-
tion, the difficulty is to design a model system that mimics exactly
the same enzymatic reaction and mechanism. The present study
examines the structure of nitroalkane oxidase (NAO) complex
with nitroethane and kinetic isotope effects at the primary and
secondary sites for the enzymatic and the uncatalyzed reaction.
The computational findings are consistent with experimental
data, suggesting that there is a differential tunneling effect for
the proton transfer reaction in NAO and in water. Analysis of
tunneling paths reveals that the enzyme reduces both the free
energy of activation and the width of the effective potential,
resulting in enhanced proton tunneling in the active site.
The flavoenzyme NAO catalyzes the conversion of nitroal-
kanes to nitrite and aldehydes or ketones (Fig. S1) (6). The
?-proton abstraction of the small substrate nitroethane by
Asp-402 is rate-limiting, which is accelerated by a factor of 109
lthough the dominant factor in enzyme catalysis is the
lowering of the quasiclassical free energy barrier of the
over the uncatalyzed reaction between nitroethane and acetate
ion in water (7).
Interestingly, the deuterium kinetic isotope effects (KIEs) are
noticeably greater for the enzymatic reaction (9.2) than that in
water (7.8) (see refs. 7, 8). Although tantalizing, the relatively
small difference in the observed KIEs is not sufficient to
conclude that there is a greater tunneling contribution in the
enzymatic process than that of the uncatalyzed reaction in water.
A number of experimental and theoretical studies suggested that
the extent of tunneling was the same in several enzymes as in
model reactions in solution (2, 9, 10), whereas other experiments
showing differential tunneling behaviors may be attributed to
different reaction mechanisms (2, 11–13). Nuclear tunneling
cannot be measured directly, and the best experimental diag-
nostic of tunneling is through measurement of kinetic isotope
effects (14). Klinman and coworkers showed that the presence
of tunneling can be revealed indirectly by a potentiated Swain-
Schaad exponent in the secondary KIEs (2, 15, 16). However,
computational studies can shed light on the extent of nuclear
quantum effects (NQE), including both zero-point energies and
tunneling contributions (3, 17). The proton transfer reaction
between nitroethane and Asp-402 catalyzed by NAO (18, 19)
provides an excellent opportunity for a comparative study be-
cause the enzymatic process (Fig. S1) can be directly modeled by
the reaction of nitroethane and acetate ion in water (Scheme 1).
Nitroalkanes represent a prototypical system for the study of
carbon acidity, which exhibit surprisingly slow deprotonation
rates compared with their high acidities (20); this phenomenon
has been termed as the nitroalkane anomaly (21, 22).
We employ a coupled free-energy perturbation and umbrella-
sampling simulation technique in Feynman centroid path inte-
gral calculations (PI-FEP/UM) to describe the NQE (23). More-
over, we adopt a combined quantum mechanical and molecular
mechanical (QM/MM) method to represent the potential energy
surface (22, 24). Thus, both the electronic structure of the
reacting system and the nuclear dynamics are treated quantum
mechanically. In our approach (23), we follow a two-step pro-
cedure (25) in which we first carry out Newtonian molecular
dynamics simulations to determine the classical mechanical
potential of mean force (PMF) along the reaction coordinate for
Author contributions: D.T.M., A.M.O., P.F.F., and J.G. designed research; D.T.M., A.H., and
M.P.V. performed research; D.T.M., A.M.O., P.F.F., and J.G. analyzed data; and D.T.M. and
J.G. wrote the paper.
The authors declare no conflict of interest.
Data deposition: The atomic coordinates for the D402N NAO plus 1-nitroethane complex
and corresponding structure factors have been deposited in the Protein Data Bank,
www.pdb.org (PDB ID code 3FCJ).
firstname.lastname@example.org, email@example.com, or firstname.lastname@example.org.
whom correspondencemaybe addressed.E-mail: email@example.com,
This article contains supporting information online at www.pnas.org/cgi/content/full/
December 8, 2009 ?
vol. 106 ?
the proton transfer reaction between nitroethane and Asp-402.
Then, atoms that are directly involved in the proton transfer
reaction are quantized, and the configurations sampled in mo-
lecular dynamics simulations are used in path-integral simula-
tions by constraining the centroid positions of the quantized
particles to the classical coordinates. This double (quantum and
classical) averaging procedure is formally exact (23, 25–28),
which yields the QM-PMF as a function of the centroid reaction
path (29, 30). In PI-FEP/UM, the ratio of the quantum partition
functions for different isotopes, which yields the KIEs, is ob-
tained by free-energy perturbation from a light isotope mass into
a heavier one within the same centroid path-integral simulation
(23), avoiding the difference between two free-energy barriers
with greater fluctuations than the difference itself for the two
isotopic reactions. Consequently, the PI-FEP/UM method is
unique in that it yields accurate results on computed KIEs,
including secondary KIEs that are not possible by other path-
integral simulation methods (23, 31). The method has been
demonstrated in a series of studies of chemical reactions in
solution and in enzymes (22, 31, 32).
Crystal Structure and Computational Model of the Michaelis Complex.
We have determined crystal structures of NAO complexes with
a series of nitroalkanes (33) including nitroethane, which is
reported here (Fig. 1A). The data collection and refinement
statistics are provided in Table S1. The experiment was designed
to provide a crucial validation of the computational method
because the Michaelis complex (MC) structure is typically not
be constructed before simulations can be carried out. Thus, we
have performed separate experimental and computational in-
vestigations of the NAO?nitroethane complex and compared the
results after each study was completed.
We used the NAO isosteric D402N mutant to trap the MC for
crystallographic analysis because it is not active with neutral
nitroalkanes (34). The 2.4-Å resolution cocrystal structure with
nitroethane demonstrates that the mutation does not signifi-
cantly perturb the active site. The electron density maps are
consistent with nitroethane located above the FAD re-face (Fig.
1A). In the crystal structure, the oxygen atoms of the R-NO2
moiety form hydrogen bonds with the ribityl 2?-OH group (3.4
and 3.7 Å). This hydrogen bonding network places the nitroeth-
ane, C?, directly ‘‘below’’ the side chain of Asn-402. Slightly
different substrate orientations are observed in each of the four
subunits in the crystal structure of the D402N nitroethane
complex (Fig. 1B). The variability likely results from a combi-
nation of real enzyme-substrate binding effects and the modest
resolution of the crystal structure. For comparison, the crystal
structures with the substrates 1-nitrohexane or 1-nitrooctane
demonstrate similar complexes, but with less binding orientation
variability (33). Thus, nitroethane exhibits the most active site
variability in the D402N complex, which correlates well with the
lower kcat/Km value relative to the longer chain nitroalkane
substrates (7, 8). This rate difference is consistent with the
shorter substrate exhibiting less potential hydrophobic interac-
tions with the enzyme than the longer chain substrates.
On the computational side, we used the 2.07-Å resolution
crystal structure of the oxidized wild-type NAO, complexed with
(19), to construct the MC model. We replaced spermine by
site with the C?atom placed ?3.5 Å from the Asp-402 side-chain
oxygen atoms (Fig. S2). These structures were minimized, fol-
lowed by 100 ps of hybrid QM/MM simulations; nine of the 10
structures converged to a unique conformation within the first
25 ps, whereas the 10th structure also reoriented after 50 ps (Fig.
1C). The MC structure is characterized by hydrogen bonding
interactions of the nitro group with the ribityl 2?-OH group and
the Asp-402 amide group, in close agreement with the
D402N?nitroethane X-ray structure. The average distance be-
tween the C? atom of nitroethane and the N5 atom of the
isoalloxazine ring is ?3.6 Å. Fig. 1D shows the superimposed
structures from X-ray diffraction and from molecular dynamics
simulations; the agreement is excellent, suggesting that our
simulation procedure can reasonably sample the conformational
subspace of the substrate in the present system.
Potential of Mean Force. The centroid (quantum mechanical)
PMFs from PI-FEP/UM simulations for the nitroethane-
deprotonation reaction in NAO (Fig. S1) and in water (Scheme
1) are shown in Fig. 2, and the computed free energies of
activation are listed in Table 1. The reaction coordinate is
defined as the difference between the breaking (donor–proton)
and forming (acceptor–proton) bond distances (Scheme 1). In
the Feynman path-integral representation (23, 27, 28), the
centroid positions of the discrete paths of quantized particles are
used to specify the reaction coordinate (29, 30). The present
PI-FEP/UM method allows for accurate KIE determination by
free energy perturbation between different isotopic masses
within a single simulation rather than separate calculations for
different isotopic reactions (23).
Fig. 2 shows that the computed free energies of activation are
15.9 and 24.4 kcal/mol for the enzymatic and the uncatalyzed
proton transfer reaction in water, respectively, which are in good
accord with the corresponding experimental results (14.0 and
24.8 kcal/mol) (7). Consequently, we estimate that NAO stabi-
Scheme 1.Proton abstraction of nitroethane by acetate ion in water.
site is in subunit D (A) and the superposition of the substrate configurations
from all four active sites are in the asymmetric unit cell (B). The 10 computa-
tional models are shown in C, and the comparison between the crystal
structure for the D402N nitroethane complex (carbon atoms in yellow) and
(carbon atoms in orange) and nitroethane (carbon atoms in yellow).
The crystal structure of the D402N-nitroethane complex. The active
Major et al.PNAS ?
December 8, 2009 ?
vol. 106 ?
no. 49 ?
lizes the transition state of the proton abstraction by 8.5 kcal/mol
from computation or 10.8 kcal/mol from experiment. The com-
puted free energy of reaction in water (7.1 kcal/mol) (22) is also
in accord with experiment (5.2 kcal/mol) (20), and the computed
free energy of reaction yields a pKa of 9.9 for nitroethane
compared with experiment (8.6) (35). In the enzyme, the relative
free energies of the MC and the product complex are nearly
identical, indicating that the acidity of nitroethane is enhanced
to a value similar to that of Asp-402. Overall, the structural and
free-energy results demonstrate that the present QM/MM and
uncatalyzed reaction in water and in NAO, allowing us to further
analyze kinetic data.
rationalized based on the principle of nonperfect synchroniza-
tion in that product stabilization by solvation lags behind the
progress of the reaction coordinate (20). Computational studies
have shown that there is little charge delocalization at the
transition state in the gas phase and that the C?rehybridization
is only 10% at the transition state for aqueous reaction (Fig. 3)
(22). The lack of redistribution of the anionic charge into the
nitro group results in poor solvation at the transition state and
an increased free-energy barrier. Fig. 3 compares the progress of
the rehybridization at the C?center as a function of the C?–?
bond order for the aqueous and enzymatic reactions. Evidently,
there is no appreciable difference in rehybridization state in the
two environments; the enzymatic process even shows somewhat
slower geometrical rearrangement than the reaction in water.
The similarity in the reaction progress demonstrates that the
observed difference in KIE is not due to change in the reaction
Kinetic Isotope Effects. The computed primary and secondary
KIEs for the nitroethane deprotonation reaction in water and in
the enzyme are listed in Table 2, along with the total KIEs that
have been determined for the perdeuterated substrate nitroeth-
ane at the C? position (7). In PI-FEP/UM simulations, the
computed NQE includes both zero-point energies and nuclear
tunneling, and their contributions to the computed KIEs are not
separable (23). Thus, it is useful to use semiclassical methods
(36) to estimate the tunneling transmission coefficient to gain an
understanding of the origin of NQE in NAO catalysis. Conse-
quently, we have used the ensemble-averaged variational tran-
sition state theory (EA-VTST), developed previously (3, 17, 37)
and successfully applied to a variety of enzyme systems (3, 17),
to separate tunneling from the overall quantum effects. The
results are listed in Table 1, in addition to the phenomenological
free energy that lowers the classical barrier due to tunneling,
Fig. 4 depicts the effective potentials (36) that include zero-
point energy of all bound vibrations except that corresponding
to the reaction coordinate for the proton transfer process in
water and in NAO. In these calculations, the minimum-energy
reaction paths were determined starting from each transition
state with the surrounding solvent and protein coordinates fixed
at the configurations in the transition state ensemble that had
been determined during the free-energy simulations (17, 37). In
Fig. 4, we show the reaction paths used to obtain the average
tunneling transmission factors. The average tunneling energies
for the deprotonation reactions in water and in the enzyme are
depicted as horizontal lines. Fig. 4 shows that the minimum-
energy paths have broad distributions, which overlap between
reaction paths for the enzymatic reaction (blue) and the uncata-
lyzed process (red); however, it is clear that the effective
potentials for the enzymatic reaction paths are more narrowly
the proton (H) in red and deuteron (D) in blue abstraction of nitroethane by
Asp-402 in nitroalkane oxidase (solid curves) and by acetate ion in water
the distances of the transferring proton (or deuteron) and the donor carbon
atom and acceptor oxygen atom. The centroid coordinates are used in path-
Table 1. Computed classical mechanical (?Gcm
proton (H) transfer reactions between nitroethane and acetate ion in water and in nitroalkane oxidase enzyme
?) and quantum mechanical (?Gqm
?) free energies of activation, total nuclear quantum
??), and the tunneling transmission coefficient (? ) and dominant tunneling energy (??Gtunn
) for the deuteron (D) and
Free energies are given in kcal/mol and tunneling transmission coefficient is unitless.
Pauling bond order (n ? n0 exp[(r0-rC-H)/c], where c ? 0.6 for transition
an indicator of the reaction progress in the enzyme (red) and in water (blue).
as the C?atom changes from an sp3tetrahedral structure into an sp2planar
configuration. The locations of the transition state are indicated by the
vertical dashed lines.
www.pnas.org?cgi?doi?10.1073?pnas.0911416106 Major et al.
distributed than those for the reactions without the catalyst. In
Fig. 4, the mass-weighted minimum-energy path in angstrom per
atomic mass unit is used to represent the reaction coordinate.
Fig. 2 shows the classical and quantum mechanical PMF for the
proton and deuteron deprotonation reactions in water and in the
enzyme, which are obtained from Newtonian molecular dynam-
ics simulations and Feynman path-integral calculations. With the
inclusion of NQE in the latter simulations (23), the computed
free energies of activation for the deuteron and proton transfer
reactions between nitroethane and acetate ion in water are,
respectively, 1.9 and 3.0 kcal/mol lower than the corresponding
‘‘classical’’ barrier (Table 1). Similar NQE has been found in
other enzymatic reactions and the corresponding uncatalyzed
reactions (3). In the enzyme, we found that NQEs are slightly
enhanced over the uncatalyzed reaction, lowering the classical
barrier by 2.1 and 3.4 kcal/mol for deuteron and proton transfer
to Asp-402. The results emphasize the importance of including
NQE in enzyme kinetics modeling to obtain accurate rate
constants (3, 17). Moreover, we note that the difference in the
free-energy barrier between the two isotopic processes is also
increased in the enzyme compared with that in solution. The
dominant factor for the enzymatic rate enhancement is transi-
tion-state stabilization by the enzyme with important contribu-
tions from the 2?-OH group of the flavin cofactor in comparison
with the uncatalyzed process in aqueous solution. The stabili-
zation effect is indicated by the difference in barrier height from
classical molecular dynamics simulations (Fig. 2). The contribu-
tions to transition-state stabilization from hydrogen bonding
interactions in the active site and the effects of the flavin
cofactor will be reported later; we focus the present study on
NQE in catalysis, which has not been quantified previously (3),
albeit, its contribution to the rate enhancement is relatively
Experimentally, the proton transfer of nitroethane to a car-
boxylate base shows a modest increase in KIE from 7.8 in water
to 9.2 in NAO (7). For comparison, the computed KIEs from
PI-FEP/UM simulations are slightly higher than the experimen-
tal data shown in Table 2, but the relative increase from water
to the enzyme is reproduced. The individual primary and
the rate-limiting step is no longer the proton transfer reaction for
larger nitroalkane substrates, whereas there is no stereoselec-
tivity for the small substrate nitroethane (7). From path-integral
and free-energy perturbation simulations, we find that the
enzymatic process has greater primary KIEs than the corre-
sponding reaction without the catalyst in water. The difference
in KIE is consistent with the free energy results shown in Fig. 2
and Table 1, where the enzymatic reaction has somewhat greater
NQE than that of the uncatalyzed reaction. However, the
secondary KIEs are smaller in NAO than in water. Interestingly,
the product of the primary and secondary deuterium KIEs in
water yields a value of 8.9, somewhat greater than the computed
value of 8.3 for the perdeuterated substrate (7, 31), suggesting
that there is slight deviation from the rule of geometric mean.
For the enzymatic reaction, the rule of geometric mean is
The finding of a larger KIE for the proton transfer reaction in
the NAO enzyme than that in water, both from PI-FEP/UM
simulations and from experiments, suggests that there is differ-
ential NQE between the catalyzed and uncatalyzed reactions.
However, the total quantum effect does not distinguish between
nuclear tunneling and zero-point effect. A diagnostic approach
that has been proposed by Klinman to assess the involvement of
tunneling contributions in enzymatic reactions (2, 15) is the use
of the mixed Swain-Schaad exponent, which describes the rela-
tionship between the H/T secondary KIE when the primary
position is occupied by hydrogen with that of D/T when the
primary position has deuterium. A value that is greater than the
semiclassical limit of 3.3 is typically attributed to the presence of
tunneling (2). Using the data in Table 2, we obtained Swain-
Schaad exponents of 3.5 and 4.3 for the proton abstraction of
nitroethane in water and in NAO, respectively. Thus, according
Table 2. Computed primary (1° ) and secondary (2° ) kinetic isotope effects, and computed
and experimental total deuterium isotope effects for the proton abstraction of nitroethane in
NAO and in water
6.63 ? 0.31
8.36 ? 0.58
1.340 ? 0.132
1.213 ? 0.150
8.3 ? 1.1
10.1 ? 1.4
13.0 ? 1.0
18.1 ? 2.4
1.375 ? 0.183
1.229 ? 0.209
7.8 ? 0.1
9.2 ? 0.4
2.17 ? 0.04
2.38 ? 0.05
1.096 ? 0.048
1.050 ? 0.025
Subscripts and superscripts are used to specify the rate constant for isotope substitutions at the primary and
secondary position, respectively.
abstraction of nitroethane by Asp-402 in nitroalkane oxidase (blue) and by
acetate ion in water (red). The reaction coordinate is the mass-weighted
distance from the transition state in angstrom per atomic mass unit. The
horizontal dashed lines indicate average dominant tunneling energies.
Effective potentials (including zero-point energies) for the proton
Major et al.PNAS ?
December 8, 2009 ?
vol. 106 ?
no. 49 ?
to this criterion, hydrogen tunneling is not significant for the
uncatalyzed reaction in water, whereas it is enhanced in the
enzymatic process. Importantly, this difference suggests that
there is differential hydrogen tunneling in the catalyzed and
To further assess tunneling effects, we used EA-VTST to
separate tunneling from the overall NQE (3, 17, 37). The
computed tunneling transmission coefficients in Table 1 are 1.3
and 3.5 for the uncatalyzed and NAO-catalyzed process, respec-
tively, implying that differential tunneling effects accelerate the
proton abstraction rate by a factor of 2.7 in catalysis. Analyses of
the dynamic trajectories correspond to the minimum-energy
reaction path with the inclusion of zero-point energy from all
bound vibrations except the degree of freedom corresponding to
the reaction coordinate (36, 37). An ensemble of reaction paths
has been obtained, starting from the transition-state ensemble
generated during the umbrella sampling simulation (3), and the
results in Fig. 4 show that the origin of enhanced tunneling may
be attributed to changes in the adiabatic potential energy surface
for the proton transfer reaction in going from aqueous solution
into the enzyme active site. Fig. 4 depicts the effective potentials
of the proton transfer trajectories for the reactions in water and
in NAO. We found that the effective potentials have a tighter
and narrower distribution in the enzyme environment than that
in aqueous solution, leading to greater average tunneling con-
tributions for the proton transfer between nitroethane and
Asp-402. On average, the tunneling paths for the enzymatic
reaction is 0.6 kcal/mol lower than that for the uncatalyzed
reaction in water from the saddle point of the effective potential
(Fig. 4 and Table 1). Of course, tunneling is also influenced by
the barrier height. In the present study, the effects of barrier
height are considered in that the minimum energy reaction paths
shown in Fig. 4 are obtained from the transition state ensemble.
The difference in NQE is a relatively small factor in catalysis in
comparison with the overall barrier reduction (8.5 kcal/mol);
however, the key finding of the present study is that there is an
unambiguous contribution from nuclear quantum effects to the
enzymatic rate enhancement in the NAO-catalyzed proton
The presence of quantum tunneling in enzymatic processes
was shown in the hydride transfer reaction catalyzed by alcohol
dehydrogenase (15). To assess tunneling contributions to catal-
ysis, it is rare that a reaction in water can be compared with the
same reaction catalyzed by an enzyme in sufficient detail (2, 12).
In the present study, we present overwhelming evidence dem-
onstrating quantitatively differential NQE that contributes to
catalysis in NAO: We found that the overall NQE has a greater
contribution to lowering the classical barrier in the enzyme, and
there is a larger difference in quantum effects between proton
and deuteron transfer for the enzymatic reaction than the
uncatalyzed one. Both experiment and computation show en-
hanced primary KIEs in the enzyme over that in water. The
mixed Swain-Schaad exponent for the enzymatic reaction is
greater than the semiclassical limit without tunneling, and it is
exacerbated relative to that in the absence of the enzyme.
Employing an entirely different computational method and
theory, we found that the tunneling transmission coefficient is
approximately three times greater for the enzyme reaction than
the uncatalyzed reaction. In addition, the origin of the difference
may be attributed to a narrowing effect in the effective potentials
for tunneling in the enzyme than that in aqueous solution. One
may argue that the rate acceleration due to hydrogen tunneling
is a small factor in NAO catalysis in comparison with the much
larger and dominating effect of the lowering of the quasiclassical
free energy barrier; however, small rate enhancement can still be
physiologically significant for an enzyme with a relatively slow
rate. Significantly, the present work demonstrates that differen-
tial quantum tunneling contributions, albeit small, are used by
the nitroalkane oxidase enzyme in catalysis.
Molecular Dynamics Free-Energy Simulations. The PMF was obtained from a
enzyme (4). Periodic boundary conditions were used along with the particle
Å3. Stochastic boundary molecular dynamics were used on one active site of the
tetrameric enzyme with a solvation sphere of 24 Å (39). Each umbrella sampling
dynamics simulations, the computed free-energy changes correspond to the
classical mechanical PMF (3). The QM-PMFs were obtained using a double aver-
aging procedure by centroid path-integral simulations on configurations saved
during the umbrella sampling (23, 25, 26). In essence, the centroid path-integral
the quantum mechanical PMFs (23, 25, 26). To evaluate the KIEs, the centroid
free-energy perturbation theory from the light mass into a heavier one (25). A
unique feature of our PI-FEP/UM method is that highly accurate KIEs, including
(23, 31). In contrast, two separated simulations are needed in other approaches
statistical fluctuations in the computed free energy barriers are typically larger
than the free energy difference, especially for secondary KIEs. Although a rea-
yield meaningful results for secondary KIEs before the development of the
PI-FEP/UM method. To our knowledge, secondary KIEs have not been reported
for enzymatic reactions from path-integral simulations. In the present study, we
quantized the donor (C?) and acceptor (O) heavy atoms and the ?-protons of
nitroethane along with atoms directly connected to them. Each quantized par-
path-integral simulations and a total of 105free-particle configurations were
sampled in each system.
For the combined QM/MM potential (24), we used a semiempirical model
that has been specifically parameterized for the proton transfer reaction
between nitroethane and acetate ion to reproduce experimental or ab initio
data at the Gaussian-3 (G3) level of theory (22). Consequently, the quality of
i.e., the intrinsic performance of the QM model, and the performance of the
QM/MM potential was validated for the solution phase reaction (31).
Ensemble-Averaged Variational Transition-State Theory. In EA-VTST calcula-
tions (3, 17, 37), we used the microcanonically optimized multidimensional
tunneling path, in which the small curvature tunneling and large curvature
dominant tunneling energy (40, 41). The transition-state ensemble was ob-
tained during the free-energy simulations for determining the PMF, and the
tunneling transmission coefficient for the enzyme was averaged over 19
reaction trajectories. The mass-weighted minimum-energy path, correspond-
ing to the steepest descent path in isoinertial coordinate of the reactants,
which are nitroethane and the side chain of Asp-402 or an acetate ion, was
optimized for each transition-state configuration in which the surrounding
solvent and protein atoms are kept frozen. The effective adiabatic potential
(Fig. 4) for locating the transition state and for computing the tunneling
transmission coefficient was obtained by adding the zero-point vibrational
energy of the reactants to the potential energy. All simulations were carried
out using the program CHARMM (c34a1) (42) and POLYRATE (43) along with
the CHARMM22 force field (44) and the TIP3P model for water (45).
Additional Details. For details of the crystal structure determination, see
Table S1. For details of initial enzyme–substrate configurations used in MC
optimization, see SI Text. In addition, all input scripts, topology, parame-
ACKNOWLEDGMENTS. We thank Professor Donald G. Truhlar for making his
POLYRATE program available. This work was supported by the National
Institutes of Health Grants GM46736 (to J.G.) and GM58698 (to P.F.F.) and by
the Offices of Biological and Environmental Research, U.S. Department of
Energy, and the National Center for Research Resources (2 P41 RR012408 to
www.pnas.org?cgi?doi?10.1073?pnas.0911416106Major et al.
A.M.O.) of the National Institutes of Health. Use of the National Synchrotron Download full-text
Light Source at Brookhaven National Laboratory was supported by the U.S.
Department of Energy Office of Basic Energy Sciences under Contract DE-
1. Garcia-Viloca M, Gao J, Karplus M, Truhlar DG (2004) How enzymes work: Analysis by
modern rate theory and computer simulations. Science 303:186–195.
2. Nagel ZD, Klinman JP (2006) Tunneling and dynamics in enzymatic hydride transfer.
Chem Rev 106:3095–3118.
3. Pu J, Gao J, Truhlar DG (2006) Multidimensional tunneling, recrossing, and the trans-
mission coefficient for enzymatic reactions. Chem Rev 106:3140–3169.
4. Gao J, et al. (2006) Mechanisms and free energies of enzymatic reactions. Chem Rev
in enzyme catalysis? J Am Chem Soc 118:11745–11751.
6. Fitzpatrick PF, Orville AM, Nagpal A, Valley MP (2005) Nitroalkane oxidase, a carban-
ion-forming flavoprotein homologous to acyl-CoA dehydrogenase. Arch Biochem
7. Valley MP, Fitzpatrick PF (2004) Comparison of enzymatic and non-enzymatic nitro-
ethane anion formation: Thermodynamics and contribution of tunneling. J Am Chem
8. Valley MP, Tichy SE, Fitzpatrick PF (2005) Establishing the kinetic competency of the
cationic imine intermediate in nitroalkane oxidase. J Am Chem Soc 127:2062–2066.
have evolved to enhance hydrogen tunneling. J Am Chem Soc 125:10877–10884.
10. Doll KM, Finke RG (2003) A compelling experimental test of the hypothesis that
enzymes have evolved to enhance quantum mechanical tunneling in hydrogen trans-
fer reactions: The ?-neopentylcobalamin system combined with prior adocobalamin
data. Inorg Chem 42:4849–4856.
11. Goldsmith CR, Jonas RT, Stack TDP (2002) C-H bond activation by a ferric methoxide
Chem Soc 124:83–96.
12. Meyer MP, Tomchick DR, Klinman JP (2008) Enzyme structure and dynamics affect
hydrogen tunneling: The impact of a remote side chain (I553) in soybean lipoxygen-
ase-1. Proc Natl Acad Sci USA 105:1146–1151.
13. Ball P (2004) By chance, or by design? Nature 431:396–397.
14. Albery WJ, Kreevoy MM (1978) Methyl transfer reactions. Adv Phys Org Chem 16:87.
15. Cha Y, Murray CJ, Klinman JP (1989) Hydrogen tunneling in enzyme reactions. Science
16. Swain CG, Stivers EC, Reuwer JF, Jr, Schaad LJ (1958) Use of hydrogen isotope effects
to identify the attacking nucleophile in the enolization of ketones catalyzed by acetic
acid. J Am Chem Soc 80:5885–5893.
Phys Chem 53:467–505.
18. Daubner SC, Gadda G, Valley MP, Fitzpatrick PF (2002) Cloning of nitroalkane oxidase
from Fusarium oxysporum identifies a new member of the acyl-CoA dehydrogenase
superfamily. Proc Natl Acad Sci USA 99:2702–2707.
19. Nagpal A, Valley MP, Fitzpatrick PF, Orville AM (2006) Crystal structures of nitroalkane
zyme trapped during turnover. Biochemistry 45:1138–1150.
20. Bernasconi CF (1992) The principle of nonperfect synchronization: More than a qual-
itative concept? Accounts Chem Res 25:9–16.
21. Kresge AJ (1974) Nitroalkane anomaly. Can J Chem 52:1897–1903.
22. Major DT, York DM, Gao J (2005) Solvent polarization and kinetic isotope effects in
Chem Soc 127:16374–16375.
23. Major DT, Gao J (2007) An integrated path integral and free-energy perturbation-
in solution and in enzymes. J Chem Theory Comput 3:949–960.
24. Gao J, Xia X (1992) A prior evaluation of aqueous polarization effects through Monte
Carlo QM-MM simulations. Science 258:631–635.
25. Sprik M, Klein ML, Chandler D (1985) Staging: A sampling technique for the Monte
Carlo evaluation of path integrals. Phys Rev B Solid State 31:4234–4244.
26. Hwang JK, Chu ZT, Yadav A, Warshel A (1991) Simulations of quantum mechanical
corrections for rate constants of hydride-transfer reactions in enzymes and solutions.
J Phys Chem 95:8445–8448.
27. Major DT, Gao J (2005) Implementation of the bisection sampling method in path
integral simulations. J Mol Graphics 24:121–127.
28. Major DT, Garcia-Viloca M, Gao J (2006) Path integral simulations of proton transfer
reactions in aqueous solution using combined QM/MM potentials. J Chem Theory
30. Cao J, Voth GA (1996) A unified framework for quantum activated rate processes. I.
General theory. J Chem Phys 105:6856–6870.
kinetic isotope effects in the proton transfer reaction between nitroethane and
acetate ion in water. J Comput Chem 29:514–522.
32. Major DT, Gao J (2006) A combined quantum mechanical and molecular mechanical
study of the reaction mechanism and ?-amino acidity in alanine racemase. J Am Chem
of intermediates in the nitroalkane oxidase reaction. Biochemistry 48:3407–3416.
34. Valley MP, Fitzpatrick PF (2003) Inactivation of nitroalkane oxidase upon mutation of
the active site base and rescue with a deprotonated substrate. J Am Chem Soc
35. Pearson RG, Dillon RL (1953) Rates of ionization of pseudo acids. IV. Relation between
rates and equilibria. J Am Chem Soc 75:2439–2443.
36. Fernandez-Ramos A, Miller JA, Klippenstein SJ, Truhlar DG (2006) Modeling the
kinetics of bimolecular reactions. Chem Rev 106:4518–4584.
37. Alhambra C, et al. (2001) Canonical variational theory for enzyme kinetics with the
protein mean force and multidimensional quantum mechanical tunneling dynamics.
Theory and application to liver alcohol dehydrogenase. J Phys Chem B 105:11326–
electrostatic interactions in combined QM/MM calculations. J Chem Theory Comput
39. Brooks CL, III, Karplus M (1989) Solvent effects on protein motion and protein effects
on solvent motion. Dynamics of the active site region of lysozyme. J Mol Biol 208:159–
40. Truhlar DG, et al. (1992) Variational transition-state theory and multidimensional,
semiclassical, ground-state transmission coefficients. Applications to secondary deu-
terium kinetic isotope effects in reactions involving methane and chloromethane. Am
Chem Soc Symp Ser 502:16–36.
41. Liu YP, Lu DH, Gonzalez-Lafont A, Truhlar DG, Garrett BC (1993) Direct dynamics
calculation of the kinetic isotope effect for an organic hydrogen-transfer reaction,
including corner-cutting tunneling in 21 dimensions. J Am Chem Soc 115:7806–7817.
42. Brooks BR, et al. (2009) CHARMM: The biomolecular simulation program. J Comput
43. Corchado JC, et al. (1998) (University of Minnesota, Minneapolis).
dynamics studies of proteins. J Phys Chem B 102:3586–3616.
45. Jorgensen WL, Chandrasekhar J, Madura JD, Impey RW, Klein ML (1983) Compar-
ison of simple potential functions for simulating liquid water. J Chem Phys 79:926–
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