Dynamics of an Enzymatic Substitution Reaction in
Kwangho Nam, Xavier Prat-Resina, Mireia Garcia-Viloca,
Lakshmi S. Devi-Kesavan, and Jiali Gao*
Contribution from the Department of Chemistry and Supercomputing Institute,
Digital Technology Center, UniVersity of Minnesota, Minneapolis, Minnesota 55455
Received October 16, 2003; E-mail: firstname.lastname@example.org
Abstract: Reactive flux molecular dynamics simulations have been carried out using a combined QM/MM
potential to study the dynamics of the nucleophilic substitution reaction of dichloroethane by a carboxylate
group in haloalkane dehalogenase and in water. We found that protein dynamics accelerates the reaction
rate by a factor of 2 over the uncatalyzed reaction. Compared to the thermodynamic effect in barrier
reduction, protein dynamic contribution is relatively small. However, analyses of the friction kernel reveal
that the origins of the reaction dynamics in water and in the enzyme are different. In aqueous solution,
there is significant electrostatic solvation effect, which is reflected by the slow reorganization relaxation of
the solvent. On the other hand, there is no strong electrostatic coupling in the enzyme and the major effect
on reaction coordinate motion is intramolecular energy relaxation.
The origin of the rate acceleration achieved by enzymes is
one of the fundamental questions in molecular biology.1While
experimental studies, including X-ray structural determination
and site-directed mutagensis, are essential to understanding the
mechanism of enzyme reactions, computer simulations can help
dissect factors that are not directly amenable by experimental
measurements and can provide insights into the specific
interactions in the active site.2-4A widely used theoretical
approach for studying enzyme catalysis is variational transition
state theory (TST),5-7which gives an upper bound to the true
classical rate constant
where k is the rate constant of a reaction, kTSTis the TST
approximation to the rate constant, and γ is the generalized
transmission coefficient.2In classical dynamics, the TST rate
constant is the rate of one-way flux through the transition state
dividing surface, which can be written as
where T is temperature, kBis Boltzmann’s constant, h is Planck’s
constant, and ∆Gqis the molar standard state quasithermody-
namic free energy of activation related to the potential of mean
force by ∆G*) w(q*) - w(qR) with q*and qRcorresponding
to the reaction coordinate at the transition state and reactant
state, respectively. The generalized transmission coefficient at
temperature T contains three components
which account for nonequilibrium effects, g(T), tunneling,
Γ(T), and trajectories that recross the transition state separating
the reactants and products, κ(T).2
According to eq 1, the rate enhancement in enzyme catalyzed
reactions can be achieved by lowering the free energy of
activation and/or by increasing the transmission coefficient in
comparison with an equivalent uncatalyzed reaction.2,8Equation
1 also provides a way of separating dynamic and thermodynamic
factors contributing to rate enhancement, although this separation
is certainly not unique because both the calculation of the
potential of mean force and the transmission coefficient depend
on the definition of the reaction coordinate, and involve protein
fluctuations.2,3,9,10Experimental and computational studies show
that the dominant factor responsible for the rate acceleration is
the reduction of the activation barrier in the enzyme,2,4,8,11which
is an equilibrium thermodynamic effect and can be attained both
by transition state stabilization and by reactant state destabiliza-
tion through interactions with specific residues in the enzyme.2,8
The role of dynamics on enzyme catalysis, which is mainly due
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k ) γkTST
γ(T) ) κ(T)Γ(T)g(T) (3)
Published on Web 01/17/2004
10.1021/ja039093l CCC: $27.50 © 2004 American Chemical Society
J. AM. CHEM. SOC. 2004, 126, 1369-1376 9 1369
to the difference in the generalized transmission coefficient2
between the catalyzed and uncatalyzed reaction, remains to be
fully understood.2,3,10,12,13In this article, we determine the
classical reflection contribution (recrossing), i.e., the κ(T) factor,2
We use the nucleophilic substitution reaction between dichlo-
roethane (DCE) substrate and Asp124 in a haloalkane dehalo-
genase (DHase)17to illustrate this computational approach
(nonequilibrium and tunneling effects are expected to be small
here), revealing differential dynamic effects for the reaction in
water and in the enzyme.
Haloalkane dehalogenases catalyze the conversion of chlo-
rinated hydrocarbons into alcohols and chloride ion through
nucleophilic displacement by Asp124 in the active site. Because
of its potential for bioremediation of environment contaminants,
it has been extensively studied17-23and has been in fact used
in applications for the treatment of contaminated soil.24,25The
effect of barrier reduction by the enzyme has been investigated
in a number of computational studies performed by modeling
the active site with the substrate dichloroethane (DCE)26-36and
by computing the potential of mean force for the nucleophilic
substitution step.37,38The catalytic mechanism has been at-
tributed to both desolvation effects32-34,38and transition state
stabilization.26-38The present study extends previous investiga-
tions by examining the dynamics of DHase in catalysis.
In what follows, we first describe computational details in
the present study, which is followed by results and discussion.
The paper concludes with a summary of major findings.
A. Model for the Enzyme-Substrate Complex. The X-ray crystal
structure of the enzyme-substrate complex (at pH 5 and 4 °C)
determined at 2.4 Å resolution (Protein Data Bank code 2DHC) was
used as the starting geometry for all simulations.17We began with a
starting configuration that was generated and fully equilibrated from a
previous study using stochastic boundary molecular dynamics simula-
tions.38The protonation states for all ionizable residues were set
corresponding to pH 7. Thus, histidine residues were modeled as neutral
residues with the proton on N? or Nδ as determined on the basis of
possible hydrogen bond interactions deduced from the X-ray crystal-
lographic structure. The resulting system has a net charge of -17 e,
which was neutralized by placing sodium cations near negatively
charged residues initially at distances greater than 17 Å from the active
center. The final protein structure was solvated with a previously
equilibrated cubic box of water molecules, centered at the geometrical
mean coordinates of the protein-substrate complex. The initial
dimension of the box was 65 × 65 × 65 Å3, which ensures that all
protein atoms are at least 10 Å away from the edges of the box. Water
molecules within 2.5 Å of any non-hydrogen atoms of the protein or
existing water were removed. The final model contains 29 540 atoms,
of which 4866 are protein atoms.
B. Potential Energy Surface. To equilibrate the solvated protein
system, we first carried out molecular dynamic simulations under
periodic boundary conditions using the all-atom CHARMM22 force
field39to represent the protein and substrate and the three-point-charge
TIP3P model for water.40
To model the chemical process, a combined quantum mechanical
and molecular mechanical (QM/MM) potential was used in all
calculations.41-43The enzyme-solvent system was partitioned into a
quantum mechanical region consisting of 15 atoms and a molecular
mechanical region containing the rest of the system. The QM system
includes eight atoms from the dichloroethane (DCE) substrate and seven
atoms from the side chain of Asp124. The QM subsystem contains
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A R T I C L E SNamet al.
1370 J. AM. CHEM. SOC.9VOL. 126, NO. 5, 2004
one boundary atom: the CRat the aspartate residue, which is represented
by the generalized hybrid orbital (GHO) method.44,45We used the
semiempirical Austin Model 1 Hamiltonian that was reparametrized
by Lau et al.34,46to specifically treat the haloalkane dehalogenase
reaction by reproducing geometrical and energetic results in comparison
with high-level ab initio data in the gas phase. The AM1-SRP model
of Lau et al. was optimized to fit the energies and barrier height obtained
from MP2/6-31+G(d) calculations. The final AM1-SRP Hamiltonian
yields an intrinsic (gas phase) barrier of 26.0 kcal/mol, which is 2.8
kcal/mol greater than the MP2 value. We note that the same model
reaction between DCE and acetate has been studied at the G2 level,
which gives a free energy barrier of 21.3 kcal/mol.38Thus, in using
the AM1-SRP, one should keep in mind that it still overestimates the
barrier height by 4.7 kcal/mol in comparison with ab initio G2 results.
Nevertheless, such a specific reaction parametrized (SRP) model yields
results with an accuracy close to the MP2 level, but it is much more
computationally efficient.34We have adopted this AM1-SRP model in
the present calculations.
C. Molecular Dynamics Simulations. To remove close contacts
and highly repulsive orientations of the initial protein-solvent system,
we first performed 100 steps of energy minimization for all water
molecules using the adopted-basis set Newton-Raphson (ABNR)
method in charmm-version c30,47with the protein atoms held fixed.
From the resulting configuration, molecular dynamics (MD) simulations
with periodic boundary conditions (PBC) and the isothermal-isobaric
(NPT) ensemble at 298 K and 1 atm were carried out to obtain the
average volume of the system. The constant pressure and temperature
calculations were carried out using charmm-c30; in this method, a
“crystal lattice” is constructed by surrounding the primary cubic cell
(the ternary complex, solvent water, and the counterions) with 26
identical images. In practice, only portions of the images within a given
distance are generated when a cutoff criterion is used to reduce the
number of nonbonded interactions, and in all the calculations of the
present study, a spherical cutoff distance of 12.0 Å was used for the
nonbonded interaction generation along with a switch function in the
region 10.5 to 11.5 Å to feather the interaction energy to zero. The
nonbonded pair list and the image list were built on the basis of group
separations, and they were updated every 25 steps and 120 steps,
respectively. During an image update, the distant solvent molecules
were replaced by a close image, and the group of image atoms within
the cutoff distance of the primary atoms was updated.
We used the leapfrog integration scheme48to propagate the equations
of motion with a time step of 1 fs and with the extended system constant
pressure and temperature algorithm implemented in charmm.49-51All
bond lengths and bond angles involving hydrogen atoms were
constrained by the SHAKE algorithm,52and the dielectric constant was
set to 1. Initially, the temperature of the system was gradually raised
from 0 to 298 K in 30 ps of molecular dynamics. Then, a further 50 ps
simulation at 298 K was carried out. The average length of the box
edge in the last 1000 steps (1 ps) of the 50 ps run was 65.543 48 Å,
which was used in the subsequent QM/MM molecular dynamics
simulations at constant volume and temperature.
The QM/MM simulations were carried out using periodic boundary
conditions and the same nonbonded cutoff, switching functions, and
dielectric constant as in the MM calculations, but we used an algorithm
that takes advantage of the minimum image convention for a periodic
cubic box. The solvent molecules (water and counterions) were
translated every 1000 steps to their image position closest to the center
of the system, which is defined as the geometric center of the protein-
ligand complex. The center of the protein-ligand complex was updated
at each nonbonded pair list update. All the hydrogen atoms were
constrained by the SHAKE algorithm. The velocity Verlet algorithm53
and the Nose ´-Hoover49,50constant temperature algorithm were used
to run these simulations at 298 K and at constant volume on the QM-
SRP/MM potential energy surface described above.
D. Potential of Mean Force Calculations. The potential of mean
force (PMF) for the dehalogenation reaction of DCE by Asp124 in
haloalkane dehalogenase was determined using the umbrella sampling
technique54-56along the mass-weighted asymmetric stretch reaction
coordinate qas, which is defined as follows
where ROCand RCClare the distances of the substrate C1carbon atom
from the nucleophilic oxygen (Asp124) and the leaving group Cl-ion,
and mOand mClare their masses. A total of 16 separate simulations (or
windows) were executed to span the entire range of the reaction
coordinate from reactants to products. Each simulation was performed
with the addition of a biasing potential, roughly the negative of the
final computed PMF, and a harmonic restraining potential centered at
the location of that particular window. For each window of these
calculations, the velocities and positions of the last configuration
generated in the previous window were used to initiate the next window,
which was equilibrated for 15 ps, and the probability density of
configurations along qaswas collected for an additional 50 ps and sorted
into bins of width 0.0025 Å. The uncertainty in the reaction coordinate
is half of the bin size, 0.00125 Å. The small bin size is due to the use
of mass-weighted reaction coordinate involving a very heavy chlorine
For comparison, exactly the same computational procedure was
executed for the model reaction of acetate ion and dichloroethane in
water. In this case, the reactants, DCE and acetate, were placed in a
cubic box of about 36.8 × 36.8 × 36.8 Å3, containing 1679 water
molecules. The reaction coordinate was defined in the same way as
the enzyme reaction in eq 4. Umbrella sampling and molecular
dynamics simulations were carried out following the same procedure
and lengths as in the enzyme case. There are no constraints of any
kind in all simulations, both for calculations in the enzyme and in
aqueous solution, and the potential of mean force was not restrained
to the first solvation layer or to a small solvent cage. Typically, there
is no observable ion-dipole complex for SN2 reactions in aqueous
solution,57-60and the results correspond to a standard state of a 1 M
concentration. Additional details of these calculations can be found in
E. Reactive Flux Trajectory Calculations. We follow the procedure
of Neria and Karplus61,62to compute the time-dependent transmission
coefficient at temperature T ) 298 K using reactive flux calculations,14-16
which is defined as
where the brackets 〈...〉*specify an equilibrium average with the reaction
(44) Gao, J.; Amara, P.; Alhambra, C.; Field, M. J. J. Phys. Chem. A 1998,
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κ(t) )〈q ˘as(0)H[qas(t) - qas
Enzym atic Substitution Reaction in Haloalkane DehalogenaseA R T I C L E S
J. AM. CHEM. SOC. 9 VOL. 126, NO. 5, 2004 1371
coordinate starting from the transition state, q ˘as(t) is the velocity of the
reaction coordinate at time t, and H(x) is a step function that equals 1
when x is positive and is 0 otherwise. The reactive flux method has
been extensively used to study reaction dynamics in solution,15,16
including SN2 reactions,63-67and has recently been applied to an enzyme
reaction (TIM).61,62We note that other approaches have also been used
to determine68or to qualitatively examine10,67κ for enzyme reactions.
First, restrained molecular dynamics simulations were performed for
the transition state, obtained from the potentials of mean force, both
for the enzyme and aqueous system. For the enzymatic reaction, the
system was first equilibrated for 15 ps, starting from a restart
configuration nearest the top of the free energy barrier. Then, an
additional 40 ps of calculations were carried out, and the coordinates
and velocities were saved at an interval of 1 ps, resulting in a total of
40 transition state configurations. For each of the 40 transition state
configurations, we propagated 100 trajectories for the reaction coor-
dinate motion. The velocities saved from the restrained molecular
dynamics simulations were used as the initial velocities to start the
trajectory calculation, except one degree of freedom corresponding to
the reaction coordinate, which was replaced by a velocity obtained from
the Boltzmann distribution at 298 K.61In other studies, the initial
velocities of all atoms of the transition state ensemble have been
randomized in trajectory calculations.15,16,63Each trajectory was propa-
gated for 100 fs, which is sufficient for computing the transmission
coefficient. To test for convergency, we performed an additional set
of calculations that generated 10 configurations separated by 10 ps in
the restrained molecular dynamics simulation, and from these configu-
rations, we also determined the time-dependent transmission coefficient.
The same procedure was carried out for the model reaction of an
acetate ion and DCE in water. In this case, the restrained molecular
dynamics simulation was run for 100 ps at the transition state, saving
one structure in every 10 ps, resulting in a total of 10 transition state
configurations. The transmission coefficient was computed based on
1000 to 4000 trajectories.
F. Molecular Dynamics with Constrained Reaction Coordinate.
To analyze factors that contribute to the total force autocorrelation
function, we computed the friction kernel at the transition state and at
the reactant state (not discussed here) from additional simulations both
in water and in the enzyme. Examination of the spectral density from
Fourier transforms of the time-correlation functions provides insights
into the difference in dynamic contributions to the enzymatic and
uncatalyzed reactions. The reaction coordinate was constrained to a
specified value during the molecular dynamics simulations using a
SHAKE-like algorithm that we have modified using Wilson’s
Cartesian to internalcoordinate
Initially, 100 ps molecular dynamics simulations were performed for
the transition state simulation. In addition, friction kernels were
computed with the symmetric internal stretch fixed or with QM/MM
electrostatic interactions excluded in 50 ps molecular dynamics
Results and Discussion
A. Potentials of Mean Force. The main goal of the present
study is to assess dynamic contributions to catalysis using
reactive flux simulations for trajectories originating from the
transition state configurations. To determine the location of the
transition state, potentials of mean force (PMF) as a function
of qaswere first determined by use of umbrella sampling for
the reaction both in DHase and in water (acetate ion was used
in the calculation in water). The computed PMFs for the
enzymatic reaction and the corresponding uncatalyzed reaction
in water using the AM1-SRP Hamiltonian34are given in Figure
1, which provides a direct comparison of the free energy barriers
of the catalyzed and uncatalyzed reaction. The transition state
is located at the highest point in the PMF, which has a value of
In aqueous solution, the computed free energy of activation
is 31.4 kcal/mol for the nucleophilic substitution reaction of
DCE by an acetate ion. The enzyme DHase lowers the activation
barrier to 20.5 kcal/mol. Recall that the AM1-SRP model
overestimates the intrinsic (gas phase) barrier by 4.7 kcal/mol.34
Taking this into account, we obtain a best estimate of the free
energy barrier of 15.8 kcal/mol for the enzyme reaction and
26.7 kcal/mol for the uncatalyzed reaction. For comparison, the
experimental free energy barrier for the dehalogenation reaction
in DHase was estimated using TST to be 15.3 kcal/mol from
the corresponding rate constant.21,22,72Early simulation results
were in the range of 1438to 16 kcal/mol.37The present AM1-
SRP QM/MM simulations show that the enzyme reduces the
free energy activation barrier by 11 kcal/mol, smaller than the
previous estimate of about 16 kcal/mol38but greater than that
estimated by Shurki et al. (8.3 to 9.4 kcal/mol).37
Experimentally, the free energy of activation for the reaction
of acetate ion with DCE in water has been determined to be
29.9 kcal/mol at 373 K,73and a free energy barrier of 28.2 kcal/
mol can be obtained using ∆G*) ∆H*- T∆S*, although it
is likely that these parameters would be temperature dependent.38
Our previous study employing the semiempirical PM3 Hamil-
*) 0.92625 Å in DHase and 0.92300 Å in water.
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Figure 1. Computed potential of mean force for the nucleophilic substitu-
tion reaction between Asp124 and 1,2-dichloroethane in the enzyme (blue)
and for the uncatalyzed reaction between an acetate ion and dichloroethane
in water (red).
A R T I C L E SNamet al.
1372 J. AM. CHEM. SOC.9VOL. 126, NO. 5, 2004
tonian for the QM region with the free energy barrier corrected
by ab initio G2 calculations yielded a value of 29.8 kcal/mol,38
in good accord with the present AM1-SRP model. For com-
parison, Shurki et al. obtained an activation free energy of 24.9
kcal/mol using an empirical valence bond potential.37These
authors reported an estimated experimental free energy barrier
of 26 kcal/mol, although the details of their extrapolation
procedure were not provided in the original paper.37These
values are certainly too low in comparison with the experimental
data from the work of Okamoto et al.73
Factors that contribute to the reduction of the free energy
barrier have been discussed previously by analyzing solvent
effects and hydrogen bonding interactions38and by computing
electrostatic contributions.37,38It is well-known that solvent
effects can increase the barrier heights for SN2 reactions as much
as 20 orders of magnitude.57,74In the present case, solvent effects
increase the free energy barrier by about 6-8 kcal/mol (from
the ion-dipole complex) for the reaction between DCE and
acetate in water.38The origin of the solvent effects was well
characterized by differential solvation effects between the
charge-localized reactant and the charge-delocalized transition
state.57,60,75In contrast, the active site of DHase contains only
one solvent water molecule, which is the nucleophile in the
subsequent deacylation step, along with two amide groups
(Glu56 and Trp125) forming hydrogen bonds with the nucleo-
phile Asp124. The major difference from the reaction in water
is that, rather than being poorly solvated at the transition state
due to charge delocalization, the transition state in the active
site enjoys increased hydrogen bonding stabilizations from two
Trp residues thanks to the development of partial negative
charges on the leaving group. In ref 38, the catalytic mechanism
of haloalkane dehalogenase was attributed to both desolvation
effects and transition state stabilization, with about equal
contribution to barrier reduction.
Bruice and co-workers used the concept of near attack
conformation (NAC) to rationalize the catalytic power of
DHase,32-34but Shurki et al. suggested that the “NAC effect”
only contributes about 2 kcal/mol to barrier reduction.37Warshel
and co-workers also carried out the most detailed analyses of
electrostatic and nonelectrostatic factors for both catalyzed and
uncatalyzed reactions. They found that solvent effects increase
the intrinsic barrier by 10.5 kcal/mol, consistent with our results,
whereas electrostatic interactions in the enzyme active site also
raise the dehalogenation barrier by 4.4 kcal/mol relative to the
gas-phase barrier,37contrary to our findings.38The latter result
of ref 37 is surprising because the barrier in the enzyme (15.3
kcal/mol) is substantially smaller than the intrinsic barrier (21.3
kcal/mol at the G2 level of theory), and it is not clear how the
barrier can be lowered in the enzyme if electrostatic interactions
increase the barrier height by 4.4 kcal/mol in the active site.
Nevertheless, solvation effects (or electrostatics) are reduced
by 6.1 kcal/mol in the enzyme active site relative to that in
B. Dynamics. Although dynamic fluctuations and protein
conformational changes76-78play an essential role in function
and catalysis and can be fully characterized by the quasither-
modynamic free energy of activation discussed above,10dynamic
contribution to catalysis is concerned with the change in the
generalized transmission coefficient between the catalyzed and
uncatalyzed reactions.2,3,9,10In ref 2, three factors have been
discussed, contributing to the generalized transmission coef-
ficient (eq 3). In the present case, quantum mechanical tunneling
is small because the dehalogenation reaction involves heavy
atoms in the bond making and breaking processes.38Further,
deviation from the equilibrium assumption in TST is expected
to be small.2,10Thus, our focus is on the effect of dynamical
recrossing, which is modeled by the reactive flux simulation
method (eq 5).14,16
Figure 2 shows the computed time-dependent transmission
coefficients for the enzymatic and aqueous reactions. The
function κ(t) equals 1 at a very short time, and it decays to a
plateau, following a short period of relaxation time during which
trajectories may recross the transition state until they all settle
into either the reactant or product state.14,16,61,63,65The plateau
value of κ(t) corresponds to the transmission coefficient for the
reaction. Figure 2 shows that κ(t) reaches the plateau value
within 30 fs for both the enzymatic and uncatalyzed reaction.
The computed κ is 0.53 for the enzymatic process, whereas it
is 0.26 for the uncatalyzed, reference reaction in water.
Interestingly, the value for the enzyme reaction is similar to
that (0.4) for a proton-transfer reaction in the enzyme triose-
phosphate isomerase.61Thus, in addition to the lowering of the
barrier height, the enzyme further accelerates the nucleophilic
substitution reaction by a factor of 2, which is substantial
kinetically. However, compared to the enormous reduction of
free energy barrier, which was computed to be 11-16 kcal/
mol,37,38protein dynamic effects (about 0.5 kcal/mol in free
energy term) make a rather small contribution to catalysis in
We have also tested the convergence of transition state
sampling in the trajectory calculations by extending the interval
of transition state configurations from 1 to 10 ps in a separate,
TS-restrained molecular dynamics simulation that lasted 100
ps for the enzyme system. We repeated similar reactive flux
calculations by running 100 trajectories for each of the 10 new
transition-state configurations, and the computed transmission
coefficient is 0.51. Thus, the effect of correlation between
different initial transition state configurations is not large in the
present dehalogenation reaction.
C. Differential Solvation Effects in Solution and in DHase.
Further insights into the chemical dynamics are obtained by
(74) Ingold, C. K. Structure and Mechanism in Organic Chemistry, 2nd ed.;
Cornell University: Ithaca, New York, 1969.
(75) Gao, J.; Garcia-Viloca, M.; Poulsen, T. D.; Mo, Y. AdV. Phys. Org. Chem.
2003, 38, 161-181.
(76) Gao, J. Curr. Opin. Struct. Biol. 2003, 13, 184-192.
(77) Hammes, G. G. Biochemistry 2002, 41, 8221-8228.
(78) Hammes-Schiffer, S. Biochemistry 2002, 41, 13335-13343.
Figure 2. Computed time-dependent transmission coefficient, κ(t), for the
reaction in water (red) and in haloalkane dehalogenase (blue).
Enzym atic Substitution Reaction in Haloalkane Dehalogenase A R T I C L E S
J. AM. CHEM. SOC. 9 VOL. 126, NO. 5, 2004 1373
examining the friction kernel η(t) of the motion of the reaction
coordinate based on a non-Markovian generalized Langevin
equation for the reaction in water and in the enzyme. This
theoretical approach has been applied to numerous systems in
the understanding of solvation effects on the dynamics of
chemical processes.63,65,79-85The friction kernel is related to
the random force, δF(t), exerted on the reaction coordinate qas
by the second fluctuation dissipation theorem80
where µ is the reduced mass of the reaction coordinate (see eq
4 for definition of the reaction coordinate). The average random
force 〈δF〉 is zero. In addition, 〈F〉 ) 0, confirming that the
calculation was carried out at the saddle point of the PMF. The
relaxation of the time-dependent friction kernel depicts the
response of solvent on the change in the reaction coordinate
and reflects the dynamical coupling of the enzyme and/or solvent
motions to the reaction coordinate motion. The time dependence
of the friction kernel contains information on solute-solvent
interactions for activated barrier crossing.84,86Examination of
the dynamical behavior and contributing factors can provide
insights into the difference in intermolecular interactions
between the reactants and the environment for the reaction in
the enzyme and in aqueous solution.
The key result in the present study is shown in Figure 3,
which depicts the autocorrelation functions (ACF) of the
fluctuation of the forces on the reaction coordinate at the
transition state for the reaction in water and in the enzyme,
which were determined by 100 ps constrained molecular
dynamics simulations. This is sufficiently long since the barrier
recrossing dynamics settles down in about 30 fs (Figure 2). Both
enzymatic and aqueous reactions experience a very rapid initial
relaxation process at a time scale of about 50 fs, but there are
major differences in the longer time behavior. In water, the fast
process is followed by a slower relaxation due to solvent
reorganization, on a time scale of 1-2 ps, consistent with that
of water reorientation motions in solution.87,88In the enzyme,
the long-time relaxation process is absent, but it is replaced by
a fast oscillation due to intramolecular symmetric stretch.
This assignment is confirmed by comparison with the ACF
of the bond distance between the nucleophilic oxygen of the
carboxylate group and the substrate carbon C1atom and between
the C1and leaving Cl atom (not shown), which is the dominant
component in the mass-weighted symmetric stretch coordinate.
Figure 4A compares the ACFs for the total fluctuating force
on the reaction coordinate constrained at the transition state and
the corresponding symmetric bond fluctuation in the enzyme
simulation. It can be seen that these two ACFs nearly coincide
with each other, with a characteristic frequency of about 150
cm-1derived from the power spectra (Figure 5). The same
comparison is made for the uncatalyzed reaction in water in
Figure 4B, which does not exhibit significant intramolecular
contributions. The results shown in Figures 3 and 4 suggest
that intermolecular hydrogen bonding interactions are dominant
in aqueous solution, whereas intramolecular correlation with the
reaction coordinate motion is significant in the enzyme (see
below), consistent with strong desolvation effects. The different
dynamic behaviors for the reaction in water and in the enzyme
are also reflected by the computed friction kernel, η(0), which
is ca. 184 kcal/g Å2in DHase and 578 kcal/g Å2in water,
revealing stronger interactions in water than those in the enzyme.
The different dynamic behaviors of enzymatic and aqueous
reactions in Figure 3 are markedly different from that for the
(79) Grote, R. F.; Hynes, J. T. J. Chem. Phys. 1980, 73, 2715-2732.
(80) Adelman, S. A. AdV. Chem. Phys. 1983, 53, 61.
(81) Verkhivker, G.; Elber, R.; Gibson, Q. H. J. Am. Chem. Soc. 1992, 114,
(82) Haynes, G. R.; Voth, G. A.; Pollak, E. J. Chem. Phys. 1994, 101, 7811-
(83) Haynes, G. R.; Voth, G. A. J. Chem. Phys. 1995, 103, 10176-10182.
(84) Neria, E.; Fischer, S.; Karplus, M. J. Chem. Phys. 1996, 105, 1902-1921.
(85) Sagnella, D. E.; Straub, J. E.; Jackson, T. A.; Lim, M.; Anfinrud, P. A.
Proc. Natl. Acad. Sci. U.S.A. 1999, 96, 14324-14329.
(86) Berne, B. J.; Tuckerman, M. E.; Straub, J. E.; Bug, A. L. R. J. Chem.
Phys. 1990, 93, 5084-5095.
(87) Mosyak, A. A.; Prezhdo, O. V.; Rossky, P. J. J. Chem. Phys. 1998, 109,
(88) Balbuena, P. B.; Johnston, K. P.; Rossky, P. J.; Hyun, J.-K. J. Phys. Chem.
B 1998, 102, 3806-3814.
Figure 3. Autocorrelation function <δF(t)δF(0)> where δF(t) is the
fluctuation in the force on the reaction coordinate at the transition state.
Figure 4. Computed autocorrelation functions for the fluctuating force on
the reaction coordinate (blue) and the symmetric stretch distance between
carbon and Asp124 nucleophilic oxygen (red) at the transition state in
haloalkane dehalogenase (A) and in water (B).
A R T I C L E SNamet al.
1374 J. AM. CHEM. SOC.9VOL. 126, NO. 5, 2004
hydride transfer reaction in liver alcohol dehydrogenase.10Villa
and Warshel using an empirical valence bond potential found
that the time-correlation functions for an energy-gap reaction
coordinate, which was derived for estimating the transmission
coefficient, were similar for the enzymatic and aqueous
processes.10They concluded that there is little difference in
dynamics for the enzyme catalyzed reaction and the uncatalyzed
reaction in water.89
The analysis of the power spectra is particularly informative.
By comparison with normal mode vibrational frequencies for
the transition state, we can identify several key vibrational modes
in the power spectra, including the symmetric stretch (150 cm-1)
and bending (266 cm-1) involving the three atoms in bond
making and breaking (note that the asymmetric stretch is the
reaction coordinate), the bending (827 cm-1) and asymmetric
stretch (1777 cm-1) of the Asp124 carboxyl group, and the
bending mode (1050 cm-1) of a methylene group in DCE. In
addition to the direct resonant coupling of the asymmetric stretch
reaction coordinate with vibrational modes of the protein bath
as a route for energy transfer, the internal vibrational modes of
the reactant also mediate energy transfer to the bath.90-93In
the enzyme (Figure 5A), the power spectrum of the friction
kernel shows significant intensities in the low-frequency region
(<100 cm-1) due to protein dynamic fluctuations, while
considerable contributions from faster modes are also observed
(e.g., the carbonyl stretch at ca. 1800 cm-1). The characteristic
fast oscillations in Figures 3 and 4a correspond to the internal
symmetric stretch at 150 cm-1with dominant intensity in the
power spectra, a strong indication of weak interactions with the
environment. On the other hand, the power spectrum of the
friction kernel in water shows major contributions from
reorientation and translation motions of the solvent water and
low intensities near the carboxyl bending and stretching modes
in high-frequency regions (Figure 5B). The intensity of the
symmetric stretch mode is also much smaller than in the enzyme.
These results demonstrate that intermolecular interactions with
water dominate energy transfer from the reaction coordinate
motion, suggesting a more direct coupling of water with the
reaction coordinate, in contrast to the enzymatic process where
intramolecular vibrations provide a main channel for coupling
the enzyme environment to the reaction coordinate.
We attribute the difference in the molecular dynamics
between the enzymatic and aqueous dehalogenation reaction to
different electrostatic environments. Previously, we and others
have found that there is a major desolvation effect in the DHase
reaction, contributing 6 to 8 kcal/mol to the reduction of the
activation barrier (see above).31-36,38Figure 3 already shows
the difference of the solvent relaxation time in water and the
significance of intramolecular symmetric stretch in the enzyme.
In Figures 6 and 7, we further examine the individual factors
that contribute to the computed ACF of the total fluctuating
force on the reaction coordinate at the transition state. We carried
out two additional simulations; in one case, both the symmetric
and asymmetric coordinates are constrained (i.e., fixing the two
distances for the breaking and forming bonds) at the transition
state, and in the second, QM/MM (i.e., reactant and environ-
ment) electrostatic interactions are excluded (of course, elec-
trostatic interactions are kept for all other parts of the system).
Figure 6 compares the ACF of the total fluctuating force on
the reaction coordinate (Figure 3) with the ACFs of the two
additional cases, at the transition state in the enzyme. When
the symmetric coordinate is also constrained, in addition to the
asymmetric reaction coordinate, the characteristic symmetric
oscillations in the total force fluctuation ACF (red curve)
vanishes (green curve in Figure 6). The long-time relaxation
(89) An anonymous referee points out a scenario, with which we fully agree,
that the absence of a difference in transmission coefficient will not
necessarily indicate that there is no dynamic effect: One can construct
models in which degrees of freedom couple to the reaction coordinate and
modulate barriers. When these degrees of freedom are turned on and off,
there will be no indication in the transmission coefficient, but they strongly
affect the rate in classical TST. See also ref 43.
(90) Bader, J. S.; Berne, B. J. J. Chem. Phys. 1994, 100, 8359-8366.
(91) Rey, R.; Hynes, J. T. J. Chem. Phys. 1996, 104, 2356-2368.
(92) Skinner, J. L.; Park, K. J. Phys. Chem. B 2001, 105, 6716-6721.
(93) Lawrence, C. P.; Skinner, J. L. J. Chem. Phys. 2003, 119, 1623-1633.
Figure 5. Power spectra of the time-correlation functions in Figure 4 for
the fluctuating force on the reaction coordinate (blue) and the symmetric
stretch distance between carbon and Asp124 nucleophilic oxygen (red) at
the transition state in haloalkane dehalogenase (A) and in water (B).
Figure 6. Computed autocorrelation function (ACF) of the force fluctuation
on the reaction coordinate at the transition state (red), and ACFs computed
with both the symmetric and asymmetric coordinate constrained (green)
and without QM/MM electrostatic interactions (blue) for the dehalogenation
reaction in the enzyme.
Enzym atic Substitution Reaction in Haloalkane DehalogenaseA R T I C L E S
J. AM. CHEM. SOC. 9 VOL. 126, NO. 5, 2004 1375
behavior due to electrostatic and van der Waals interactions in Download full-text
the symmetric stretch constraint is not further assessed here,
but the fast dynamic fluctuations of other amino acid residues
in the active site that affect the electrostatic interactions with
the QM region are apparent in the green curve. However, the
signature of these interactions only shows up after the dominant
intramolecular motion is frozen. When electrostatic interactions
between the QM and MM regions are excluded in the simulation
(blue curve), the symmetric stretch motion remains, and a very
long relaxation process due to van der Waals interactions is
Turning to similar comparisons for the uncatalyzed reaction
in water in Figure 7, we found that the solvent relaxation time
in the ACF obtained with both the symmetric and asymmetric
coordinates constrained (green) is about twice as long as that
for the ACF of the total fluctuating force on the asymmetric
coordinate (red). Clearly, the symmetric vibration helps energy
transfer between the solute and solvent as well, which enhances
the water reorientation process in the first solvation layer. This
is reflected by the corresponding power spectra in Figure 8 (the
high frequency region has very low intensity and is not shown
for clarity), in which the intensity is severely reduced even in
the very low-frequency region (green) in the case where both
the symmetric and asymmetric coordinates are constrained.
When the electrostatic interactions between the QM and MM
regions are screened out (blue), we see that the intensity
corresponding to the internal symmetric stretching motions
increases (Figure 7). Interestingly, the impact of the solvent
libration motions on solute-solvent coupling is not significantly
affected in this case. This is because the dynamics of the
environment is similar, and it is effectively coupled to the QM
region through van der Waals interactions.
It is interesting to compare the power spectra obtained for
the enzymatic reaction with different constraints and excluding
QM/MM electrostatic interactions (Figure 9). When QM/MM
electrostatic interactions are removed (blue), the symmetric
stretch is red-shifted by about 15 wavenumbers. However, when
both the symmetric and asymmetric coordinates are fixed at
the transition state, the protein dynamical fluctuations are not
reflected in the power spectra, and there is no coupling with
the protein environment at the low-frequency regions as opposed
to the situation in water, in which weaker coupling is still
apparent under the same constraints (Figure 8). This further
shows the differential environment effects on reaction coordinate
motions in water and in the enzyme.
In conclusion, we have studied the dynamics of the nucleo-
philic substitution reaction of DCE by a carboxylate group in
DHase and in water using combined QM/MM potential and
reactive flux molecular dynamics simulation methods. We found
that protein dynamics accelerates the reaction rate by a factor
of 2 over the uncatalyzed reaction or lowers the free energy
barrier by about 0.5 kcal/mol. However, in comparison with
the large thermodynamic effect in barrier reduction (about 11
to 16 kcal/mol),37,38protein dynamic contribution is rather small.
This conclusion is in agreement with previous findings for other
enzyme systems.2,3,10The discovery in the present study is that
the origins of the reaction dynamics for the uncatalyzed process
in water and the catalyzed reaction in the enzyme are different
from analyses of the friction kernel for the reaction coordinate
motions. In aqueous solution, there is a significant electrostatic
solvation effect, which is reflected by the slow reorganization
relaxation of the solvent. On the other hand, there is no strong
electrostatic coupling in the enzyme and the major effect on
reaction coordinate motion is intramolecular energy relaxation.
Acknowledgment. We thank the National Institutes of Health
for support of our research on enzyme catalysis. We also thank
Professors Martin Karplus and Donald G. Truhlar for insightful
comments on an early version of this manuscript.
Figure 7. Computed autocorrelation function (ACF) of the force fluctuation
on the reaction coordinate at the transition state (red), and ACFs computed
with both the symmetric and asymmetric coordinate constrained (green)
and without QM/MM electrostatic interactions (blue) for the nucleophilic
substitution reaction between dichloroethane and acetate ion in water.
Figure 8. Fourier transform of the autocorrelation functions in Figure 7
for the dehalogenation reaction in water.
Figure 9. Fourier transform of the autocorrelation functions in Figure 6
for the dehalogenation reaction in the enzyme.
A R T I C L E SNamet al.
1376 J. AM. CHEM. SOC.9VOL. 126, NO. 5, 2004