Báo cáo Y học: Barrier passage and protein dynamics in enzymatically catalyzed reactions docx

MINIREVIEW
Barrier passage and protein dynamics in enzymatically catalyzed
reactions
Dimitri Antoniou
1
, Stavros Caratzoulas
1,
*, C. Kalyanaraman
1
, Joshua S. Mincer
1
and Steven D. Schwartz
1,2
1
Department of Biophysics, Albert Einstein College of Medicine, Bronx, NY, USA;
2
Department of Biochemistry, Albert Einstein
College of Medicine, Bronx, NY, USA
This review describes studies of particular enzymatically
catalyzed reactions to investigate the possibility that catalysis
is mediated by protein dynamics. That is, evolution has
crafted the protein backbone of the enzyme to direct vibra-
tions in such a fashion to speed reaction. The review presents
the theoretical approach we have used to investigate this
problem, but it is designed for the nonspecialist. The results
show that in alcohol dehydrogenase, dynamic protein
motion is in fact strongly coupled to chemical reaction in
such a way as to promote catalysis. This result is in concert
with both experimental data and interpretations for this and
other enzyme systems studied in the laboratories of the two
other investigators who have published reviews in this issue.

Keywords: protein dynamics; enzyme catalysis; tunneling;
promoting vibration; promoting mode.
INTRODUCTION
The transmission of an atom or group of atoms from the
reactant region of a reaction to the product region under the
control of an enzyme is central to biochemistry. The manner
in which the enzyme speeds this transfer is in some cases still
not clear. What is known is the end effect; enzymatic
reactions occur at rates many orders of magnitude more
rapid than the corresponding solution phase reactions. This
review will describe work recently completed in our group
that has focused on examining the possibility that protein
dynamics may in some enzymes play a central role in helping
to produce the catalytic effect. These types of motions,
which we have termed Ôrate promoting vibrationsÕ,are
motions of the protein matrix that change the geometry of
the chemical barrier to reaction. By this we mean that both
the height and width of the barrier are changed. This unique
role for the protein matrix has significant implications for
the dynamics of the chemical reaction; in particular, causing
a barrier to narrow can significantly enhance a light
particle’s ability to tunnel, while masking the normal kinetic
indicators of such a phenomenon. It is this feature that we
have proposed as a unifying principle for some experimental
data relating to tunneling in enzymatic reactions.
This paper will describe our studies of rate promoting
vibrations in enzymatic reactions with particular attention
to the physical origins of the phenomenon. The structure of
this paper will be as follows: in the next section, we will
briefly review a number of different potential mechanisms

for enzyme catalytic action along with promoting vibra-
tions. Following this, we will describe the mathematical
foundation for our theories in some detail. This section will
be written for nonexperts, but will contain the necessary
formulae for the specialist as well. It will include the
relationship between the current theories and a well-known
approach to charged particle transfer in biological reactions,
namely the Marcus theory. In this section we will also
describe a simple nonbiological chemical system in which
the physical features of promoting vibrations may be easily
understood – proton transfer in organic acid crystals. We
will then describe how we have used these concepts to fit
seemingly anomalous kinetic data for enzymatic reactions.
In the next section, we explore how one might rigorously
identify the presence of such a promoting vibration in any
enzymatic reaction, and illustrate the concepts with appli-
cations to specific enzyme systems. The paper then con-
cludes with discussions of future directions for this research.
POTENTIAL MODES OF ENZYMATIC
ACTION
The exact physical mechanisms by which enzymes cause
catalysis is still a topic for vigorous dialogue [1–3]. The
research described in this paper will argue for a strong
contribution from a nontraditional source, i.e. directed
protein motions. In order to place this concept into a
context, we will briefly review other potential mechanisms
for enzymes to cause catalysis. We emphasize that none of
these mechanisms are mutually exclusive, and are probably
all involved in catalysis to a greater or lesser extent in each
enzyme system.

One of the earliest and still widely accepted ideas used to
explain this catalytic efficiency is the transition state-binding
concept of Pauling [4]. In this picture, as a chemical
substance is being transformed from reactants to products,
the species that binds most strongly to the enzyme is at some
Correspondence to S. D. Schwartz, 1300 Morris Park Ave.,
Bronx, NY 10461, USA. Tel.: + 1 718 430 2139,
E-mail:
Abbreviations: NAC, near attack conformations; HLADH, horse liver
alcohol dehydrogenase; YADH, yeast alcohol dehydrogenase.
Note: a website is available at />faculty/schwartz.htm
*Present address: Department of Chemical Engineering, Princeton
University, NJ, USA.
(Received 8 March 2002, revised 31 May 2002, accepted 6 June 2002)
Eur. J. Biochem. 269, 3103–3112 (2002) Ó FEBS 2002 doi:10.1046/j.1432-1033.2002.03021.x
intermediate point thought to be at or near the top of the
solution phase (i.e. uncatalyzed) barrier to reaction. This
preferential binding releases energy that stabilizes the
transition state and thus lowers the barrier to reaction. This
is a standard picture for nonbiological catalysis, and it also
has significant experimental support. A critical observation
is found using kinetic isotope effect methods. In this way,
one can probe the chemical structure of the transition state
in the catalytic event. Stable molecules can be designed that
share the electronic properties of the transition state (usually
identified by the electrostatic potential at the van der Waals
surface). Furthermore, these molecules make highly potent
inhibitors [5,6]. When substrate-like molecules that cannot
react to form products bind, often a far lower level of
inhibition is found. This result is said to be indicative of the

fact that the transition state is strongly bound. It has been
argued, however, that the electrostatic character of the
active site during the catalytic event is largely determined by
whatever charge stabilization is needed as the reaction
progresses. If an inhibitor is designed with the complement-
ary charges, it will bind strongly to the active site. However,
this does not imply that the method by which the enzyme
produced catalysis was transition state binding and con-
comitant release of energy [1].
A second approach, which might be viewed as the
converse of transition state stabilization, is ground state
destabilization. In this picture [7], the role of the enzyme is to
make the reactants less stable rather than making the
transition state more stable. Thus the energetic hill that must
be climbed with thermal activation is lowered. Energies are
all relative and so the end effect of this and the first
mechanism are the same; lowering the relative energy
difference between reactants and transition state. But it is
clear that this view presents a very different physical
mechanism. Recent calculations [8] seem to show that this
model may well be dominant for the most efficient enzyme
known, orotidine monophosphate decarboxylase.
A third concept that has been also suggested. In solution,
reactants are strongly solvated by water, the dominant
component of most living cells. When enzymes bind
reactants, they often exclude water, and this lowered
dielectric environment may be more conducive to reaction
[9–11]. This approach to catalysis tends to treat the catalytic
event much like an electron transfer reaction in solution.
The dominant description of electron transfer in solution is

Marcus’ theory [12], and this approach has also been used to
describe atom transfer [13]. The concept here is that the
main barrier to reaction is, in fact, reorganization of the
solvent as charged particles move, rather than the intrinsic
chemical barrier due to transformation of the substrate. It is
certainly true that such energy reorganization may be a
significant component in many cases, but probably does not
account for all catalysis in biological systems.
A fourth recent suggestion by Bruice [14,15] is that the
dominant role of an enzyme is to position substrates in such
a way that thermal fluctuations easily take them over the
barrier to reaction. The set of positions the enzyme
encourages the substrate to take are known as Ônear attack
conformationsÕ (NACs). Here, while the enzyme might bind
strongly to a transition state structure, this binding energy is
not thought to be released specifically to speed the reaction.
The enzyme moulds the substrate so that it is on the edge of
reacting and forming products. Because the enzyme helps
the reactants to form the NAC, this view is philosophically a
bit closer to the ground state destabilization view. It is,
however, not a statistical energetic argument, but rather a
chemical structure argument.
A fifth possibility for the mode of action of enzymes is the
principle subject of this paper, that is, motions within the
protein itself actually speed the rate of a chemical reaction.
There is significant relation between this possibility and the
last view of catalysis described above, i.e. the creation of the
NAC. It must be stressed, however, that the current view is a
dynamic one. For this concept to be true, actual motions of
the protein must couple strongly to a reaction coordinate

and cause an increase in reaction rate. This is not simply
preparation of a reactive species, but rather dynamic
coupling. It is important to note that this is an entirely
different view of the method by which the enzyme
accomplishes rate acceleration. In this view, evolution has
created a protein structure that moves in such a way as to
lower a barrier and make it less wide. It must be emphasized
that this lowering of the barrier is not statistical lowering of
a potential of mean force through the release of binding
energy, but rather the use of highly directed energy (a
vibration) in a specific direction. Furthermore, this is not
simply the statistical preparation of reactive species as in the
NAC concept. Here, protein dynamics directly affect the
reaction coordinate potential. Although this effect can be
quite apparent for a tunneling system (the probability to
tunnel increases exponentially with a reduction of the width
of the tunneling barrier), it is equally important for systems
where the reaction proceeds through classical transfer,
because as the barrier is made narrower, it is also lowered.
In order to understand how directed protein motions may
cause catalysis, we need a theory of chemical reactions in a
condensed phase. Our group has developed theories over
the past 10 years, and this work, initially developed for
simple condensed phases, such as polar media, forms the
basis for our analysis. We now describe these theories in
some detail.
AN ENZYME AS A CONDENSED PHASE:
THEORETICAL FORMULATION FOR
THE STUDY OF CHEMICAL REACTION
There are two requirements to enable the study of a

chemical reaction in any system, be it as simple as a gas
phase collision, or as complex as that in an enzyme. First, a
potential energy for the interaction of all the atoms in the
system is needed. This includes the interactions of all atoms
having their chemical bonds changed, and those that do not.
The second requirement is for a method to solve the
dynamics of the equations of motion that allow one to
follow the progress of the reacting species in the presence of
the rest of the system from reactants to products. In this
work, we assume that we are able to obtain the first
requirement (the potential). In order to study the dynamics
on this potential, however, one needs to solve the Schro-
dinger equation for the entire collection of atoms. It is a
well-known fact that this is difficult for three or four atoms,
and so essentially impossible for the thousands of atoms in a
reaction catalyzed by an enzyme.
Various groups have taken a number of possible
approaches to solve this problem. One may assume that
quantum effects are minor, and use a purely classical
3104 D. Antoniou et al. (Eur. J. Biochem. 269) Ó FEBS 2002
approach to solve the dynamics [16]. We are specifically
interested in studies of enzyme systems where quantum
mechanics plays a significant role, through tunneling of a
light particle, in the chemical step of the enzyme, and so the
classical approach will not be expected to yield valid results.
Another approach is to use a mixed quantum-classical
formulation in which a subset of the atoms is treated
quantum mechanically and the rest of the system is treated
purely classically. In recent years, this approach has become
popular with the pioneering work of such investigators as

Gao [8]. We have chosen a different approach, largely on
stylistic grounds. Rather than treating the full collection of
atoms as a mixture of quantum and classical objects
(something that is difficult to define rigorously), we have
developed approximate approaches to treat the entire
collection of atoms as a quantum mechanical entity. As
mentioned above, both approaches are approximate, but we
prefer to make the approximation uniform for the entire
system.
We have called our approach the ÔQuantum KramersÕ
methodology [17,18]. Our ideas were motivated by the
following approximations developed for the study of the
classical mechanics of large, complex systems. It is known
that for a purely classical system [19,20], an accurate
approximation of the dynamics of a tagged degree of
freedom (for example a reaction coordinate) in a condensed
phase can be obtained through the use of a generalized
Langevin equation. The generalized Langevin equation is
given by Newtonian dynamics plus the effects of the
environment in the form of a memory friction and a random
force [21]. Thus, all the complex microscopic dynamics of all
degrees of freedom other than the reaction coordinate are
included only in a statistical treatment, and the reaction
coordinate plus environment is treated as a modified one-
dimensional system. What allows a realistic simulation of
complex systems is that the statistics of the environment can
in fact be calculated from a formal prescription. This
prescription is given by the Ôfluctuation-dissipation the-
oremÕ, which yields the relationship between friction and
random force. In particular, this theory enables us to

calculate the memory friction from a relatively short-time
classical simulation of the reaction coordinate. The Quan-
tum Kramers approach, in turn, is dependent on an
observation of Zwanzig [22,23]; if an interaction potential
for a condensed phase system satisfies a fairly broad set of
mathematical criteria, the dynamics of the reaction coordi-
nate as described by the generalized Langevin equation can
be rigorously equated to a microscopic Hamiltonian in
which the reaction coordinate is coupled to an infinite set of
Harmonic Oscillators via simple bilinear coupling:
H ¼
P
2
s
2m
s
þ V
o
þ
X
k
P
2
k
2m
k
þ
1
2
m

k
x
2
k
q
k
À
c
k
s
m
k
x
2
k

2
ð1Þ
The first two terms in this Hamiltonian represent the kinetic
and potential energy of the reaction coordinate, and the last
set of terms similarly represent the kinetic and potential
energy for an environmental bath. Here, s represents some
coordinate that measures progress of the reaction (for
example, in alcohol dehydrogenase where the chemical
step is transfer of a hydride, s might be chosen to represent
the relative position of the hydride from the alcohol to the
NAD cofactor.) c
k
is the strength of the coupling of the
environmental mode to the reaction coordinate, and m

k
and x
k
give the effective mass and frequency, respectively,
of the environmental bath mode. A discrete spectral density
gives the distribution of bath modes in the harmonic
environment:
JðxÞ¼
p
2
X
k
c
2
k
m
k
x
k
dðx À x
k
ÞÀdðx þ x
k
Þ
½
ð2Þ
Here d(x ) x
k
)istheÔDirac deltaÕ function, so the spectral
density is simply a collection of spikes, located at the

frequency positions of the environmental modes, weighted
by the strength of the coupling of these modes to the
reaction coordinate. Note that this infinite collection of
oscillators is purely fictitious; they are chosen to reproduce
the overall physical properties of the system, but do not
necessarily represent specific physical motions of the atoms
in the system. It would seem that we have not made a huge
amount of progress; we began with a many-dimensional
system (classical) and found out that it could be accurately
approximated by a one-dimensional system in a frictional
environment (the generalized Langevin equation.) We have
now recreated a many-dimensional system (the Zwanzig
Hamiltonian). The reason we have done this is twofold.
First, there is no true quantum mechanical analogue of
friction, and so there really is no way to use the generalized
Langevin approach for a quantum system, such as we
would like to do for an enzyme. Second, the new quantum
Hamiltonian given in Eqn (1) is much simpler than the
Hamiltonian for the full enzymatic system. Harmonic
oscillators are a problem that can easily be solved by
quantum mechanics. Thus, the prescription is, given a
potential for the enzymatic reaction, we model the exact
problem using Zwanzig Hamiltonian, as in Eqn (1), with
the distribution of harmonic modes given by the spectral
density in Eqn (2), and found through a simple classical
computation of the frictional force on the reaction coordi-
nate. Then, using methods to compute quantum dynamics
developed in our group [24–29], quantities such as rates or
kinetic isotope effects may be computed. Thus, the quantum
Kramers method, developed in our group, consists of the

following ingredients. Given a potential for the enzymatic
reaction, we model the exact problem using Zwanzig’s
Hamiltonian, as in Eqn (1), with the distribution of
harmonic modes given by the spectral density in Eqn (2).
The spectral density is obtained through a Ômolecular
dynamicsÕ simulation of the classical system. Then, using
methods developed in our group to carry out the quantum
dynamics, quantities such as rates or kinetic isotope effects
may be computed.
This approach enables us to model a variety of condensed
phase chemical reactions with essentially experimental
accuracy [30]. There are deeper connections between this
approach and another popular method of dynamics com-
putation in complex systems. We have shown [30] that this
collection of bilinearly-coupled oscillators is in fact a
microscopic version of the popular Marcus theory for
charged particle transfer [12,13]. The bilinear coupling of the
bath of oscillators is the simplest form of a class of couplings
that may be termed antisymmetric because of the mathe-
matical property of the functional form of the coupling on
reflection about the origin. This property has deeper
implications than the mathematical nature of the symmetry
Ó FEBS 2002 Barrier passage and protein dynamics (Eur. J. Biochem. 269) 3105
properties. Antisymmetric couplings, when coupled to a
double-well-like potential energy profile, are able to instan-
taneously change the level of well depths, but do nothing to
the position of well minima. This modulation in the position
of minima is exactly what the environment is envisaged to
do within the Marcus theory paradigm. As we have shown
[30], the minima of the total potential in Eqn (1) will occur,

for a two-dimensional version of this potential, when the q
degree of freedom is exactly equal and opposite in sign to
cs
mx
2
, and the minimum of the potential energy profile along
the reaction coordinate is unaffected by this coupling.
Within Marcus’ theory, which is a deep tunneling theory,
transfer of the charged particle occurs at the value of the
bath coordinates that cause the total potential to become
symmetrized. Thus, if the bare reaction coordinate potential
is symmetric, then the total potential is symmetrized at the
position of the Ôbath plus couplingÕ minimum. When this
configuration is achieved, the particle tunnels; the activation
energy for the reaction is largely the energy to bring the bath
into this favorable tunneling configuration.
While Marcus’ theory and our microscopic quantum
Kramers theory are highly successful in many cases, in other
cases, it is not possible to reproduce experimental results
using such an approach. The reason for this is that the
antisymmetric coupling contained within the Zwanzig
Hamiltonian does not physically represent all possible
important motions in a complex reacting system. In fact,
such a reality was pointed out some time ago in seminal
work of the Hynes group [31]. In some of our earlier work
on hydrogen transfer in enzymatic systems, we were able to
show that one could reasonably fit experimental kinetic data
in such enzymatic systems with phenomenological applica-
tion of the Hynes theories [32]. We became interested in a
microscopic study of such systems in the examination of

nonbiological proton transfer reactions, i.e. organic acid
crystals. The simplest example is a carboxylic acid dimer,
showninFig.1.Suchsystemshadbeenstudiedformany
years [33–37], and they presented what seemed to be a
chemical physics conundrum. While quantum chemistry
computations seemed to show that the intrinsic barrier to
proton transfer in these systems was reasonably high, and
low experimental activation energies seemed to indicate a
significant involvement of quantum tunneling in the proton
transfer mechanism, careful measurements of kinetic iso-
tope effects showed kinetics indicative of classical transfer.
In order to study such systems, a rigorous theory, which
allowed inclusion of symmetrically coupled vibrations, in
addition to an environmental bath of antisymmetrically
coupled oscillators, was needed. Mathematically, the simp-
lest transformation of the Hamiltonian in Eqn (1) is given
by:
H ¼
P
2
S
2m
s
þ V
o
þ
X
k
P
2

k
2m
k
þ
1
2
m
k
x
2
k
q
k
À
c
k
s
m
k
x
2
k

2
þ
P
2
Q
2M
þ

1
2
mX
2
Q À
Cs
2
MX
2

ð3Þ
Note that in this case, the oscillator that is symmetrically
coupled, represented by the last term in Eqn (3), is in fact a
physical oscillation of the environment.
We were able to develop a theory [38] of reactions
mathematically represented by the Hamiltonian in Eqn (3),
and using this method and experimentally available param-
eters for the benzoic acid proton transfer potential, we were
able to reproduce experimental kinetics as long as we
included a symmetrically coupled vibration [39]. The results
are shown in Table 1 below. The two-dimensional activa-
tion energies refer to a two-dimensional system comprised
of the reaction coordinate and a symmetrically coupled
vibration. The reaction coordinate is also coupled to an
infinite environment as described above.
In this case, the symmetric motion has a clear physical
origin: the symmetric motion of the carbonyl and hydroxyl
oxygen atoms toward each other. Kinetic isotope effects in
this system are modest, even though the vast majority of the
proton transfer occurs via quantum tunneling. The end

result of this study is that symmetrically coupled vibrations
can significantly enhance rates of light particle transfer, and
also significantly mask kinetic isotope signatures of tunnel-
ing. A physical origin for this masking of the kinetic isotope
effect may be understood from a comparison of the two-
dimensional problem comprised of a reaction coordinate
coupled symmetrically and antisymmetrically to a vibration.
As Fig. 2 shows, antisymmetric coupling causes the minima
(the reactants and products) to lie on a line; the minimum
energy path, which passes through the transition state. In
contrast, symmetric coupling causes the reactants and
products to be moved from the reaction coordinate axis in
such a way that a straight line connection of reactant and
products would pass no where near the transition state.
This, in turn, results in the gas phase physical chemistry
phenomenon known as corner cutting [40–42]. Physically,
the quantity to be minimized along any path from reactant
to products is the action. This is an integral of the energy,
and so loosely speaking, it is a product of distance and depth
under the barrier that must be minimized to find an
approximation to the tunneling path. The action also
includes the mass of the particle being transferred, and so in
the symmetric coupling case, a proton will actually follow a
very different physical path from reactants to products in a
reaction than a deuteron. (Not just in the trivial sense that
one tunnels more than another). It is this following of a
different physical path, even when tunneling dominates,
Fig. 1. A benzoic acid dimer. Thereactioncoordinateinthiscaseisthe
symmetric transfer of the hydroxyl protons to the carbonyl oxygen.
The promoting vibration is the symmetric motion of the oxygens

toward each other.
Table 1. Activation energies for H and D transfer in benzoic acid
crystals at T ¼ 300 K. Three values are shown: the activation energies
calculated using a one- and two-dimensional Kramers problem and the
experimental values. The values of energies are in kcalÆmol
)1
.
E
1d
E
2d
Experiment
H 3.39 1.51 1.44 kcalÆ mol
)1
D 5.21 3.14 3.01 kcalÆ mol
)1
3106 D. Antoniou et al. (Eur. J. Biochem. 269) Ó FEBS 2002
that causes the kinetic isotope effects to be masked. It was
this low level of primary kinetic isotope effect that suggested
a similarity between the proton transfer mechanism in the
organic acid crystal and that of enzymatic reactions. While
coupled motions of nearby atoms in enzymatic reactions
have been used to explain anomalous kinetic isotope effects
[43], these were studies in a classical picture with semiclas-
sical tunneling added (the Bell correction; [44]) and they
could not be used to account for enzymatic reactions in a
deep tunneling regime.
Klinman and coworkers have helped pioneer the study of
tunneling in enzymatic reactions. One focus of their work
has been the alcohol dehydrogenase family of enzymes.

Alcohol dehydrogenases are NAD
+
-dependent enzymes
that oxidize a wide variety of alcohols to the corresponding
aldehydes. After successive binding of the alcohol and
cofactor, the first step is generally accepted to be complex-
ation of the alcohol to one of the two bound Zinc ions [45].
This complexation lowers the pK
a
of the alcohol proton and
causes the formation of the alcoholate. The chemical step is
then transfer of a hydride from the alkoxide to the NAD
+
cofactor. They [46] have found a remarkable effect on the
kinetics of yeast alcohol dehydrogenase (a mesophile) and a
related enzyme from Bacillus stereothermophilus, a thermo-
phile. A variety of kinetic studies from this group have
found that the mesophile [47] and many related dehydro-
genases [48–51] show signs of significant contributions of
quantum tunneling in the rate-determining step of hydride
transfer. Remarkably, their kinetic data seem to show that
the thermophilic enzyme actually exhibits less signs of
tunneling at lower temperatures. Recent data of Kohen &
Klinman [52] also show, via isotope exchange experiments,
that the thermophile is significantly less flexible at mesophi-
lic temperatures, as in the results of Petsko et al. [53], who
conducted studies of 3-isopropylmalate dehydrogenase
from the thermophilic bacteria Thermus thermophilus.These
data have been interpreted in terms of models similar to
those we have described above, in which a specific type of

protein motion strongly promotes quantum tunneling; thus,
at lower temperatures, when the thermophile has this
motion significantly reduced, the tunneling component of
reaction is hypothesized to go down even though one would
normally expect tunneling to go up as temperature goes
down. Additionally, the Klinman group has investigated the
catalytic properties of various mutants of horse liver alcohol
dehydrogenase (HLADH). HLADH in the wild-type has a
slightly less advantageous system to study than yeast
alcohol dehydrogenase, because the chemistry is not the
rate determining step in catalysis for this enzyme. Two
specific mutations have been identified, Val203 fi Ala and
Phe93 fi Trp, which significantly affect enzyme kinetics.
Both residues are located at the active site; the valine
impinges directly on the face of the NAD
+
cofactor distal to
the substrate alcohol. Modification of this residue to the
smaller alanine significantly lowers both the catalytic
efficiency of the enzyme, as compared to the wild-type,
and also significantly lowers indicators of hydrogen tunnel-
ing [54]. Phe93 is a residue in the alcohol binding pocket.
Replacement with the larger tryptophan makes it harder for
the substrate to bind, but does not lower the indicators of
tunneling [55]. Bruice’s recent molecular dynamics calcula-
tions [56] produce results consistent with the concept that
mutation of the valine changes protein dynamics, and it is
this alteration, missing in the mutation at position 93, which
in turn changes tunneling dynamics. (We note the recent
experimental results from Klinman’s group [57] in which no

decrease in tunneling is seen as the temperature is raised.)
A final set of enzymes now thought to exhibit dynamic
protein control of tunneling hydrogen transfer is that in the
amine dehydrogenase family. Scrutton and coworkers have
extensively studied these enzymes [58]. Though similarly
named and having a similar end effect as the alcohol
dehydrogenases, they employ radically different chemistry.
These enzymes catalyze the oxidative deamination of
primary amines to aldehydes and free ammonia. In this
case, however, rather than a chemical step of hydride
transfer, the rate determining chemical step is proton
transfer; and in fact these enzymes catalyze a coupled
electron proton transfer reaction. Electrons are coupled to
some cofactor, for example, in the case of aromatic amine
dehydrogenase, the cofactor is tryptophan-tryptophyl qui-
none. Kinetic studies have shown that methylamine dehy-
drogenase exhibits not only relatively large primary kinetic
isotope effects (unlike the alcohol dehydrogenases), but also
very strong temperature dependence in the measured
activation energy. This experimental data has been inter-
preted as showing that the enzyme works via a promoting
vibration [59], as we have suggested for bovine serum amine
oxidase [32], and for various forms of HLADH [60]. Here,
the primary kinetic isotope effect is % 17, rather than 3 or 4.
s
q
s
0
+s
0

A,S
S
A
Fig. 2. This diagram shows the location of stable minima in two-
dimensional systems. In one case a vibrational mode is symmetrically
coupled to the reaction coordinate, and in the other, antisymmetrically
coupled. The figure represents how antisymmetrically and symmetri-
cally coupled vibrations effect position of stable minima – that is
reactant and product wells – in modulating the one dimensional double
well potential (before coupling along the x axis). The x axis, s,repre-
sents the reaction coordinate, and q the coupled vibration. The points
on the figure labeled S and A are the positions of the well minimal in
the two dimensional system with symmetric and antisymmetric coup-
ling, respectively. An antisymmetrically coupled vibration displaces
those minima along a straight line, so that the shortest distance
between the reactant and product wells passes through the transition
state. In contradistinction, a symmetrically coupled vibration, allows
for the possibility of Ôcorner cuttingÕ under the barrier. For example, a
proton and a deuteron will follow different paths under the barrier.
Ó FEBS 2002 Barrier passage and protein dynamics (Eur. J. Biochem. 269) 3107
Another enzyme studied by this group is aromatic amine
dehydrogenase. This enzyme is especially interesting because
it is fairly nonspecific in the substrates it will bind and
catalyze. In particular, in the series benzylamine, dopamine,
and tryptamine, primary kinetic isotope effects range from a
low of 4.8 in benzylamine to a high of 54.7 in tryptamine
[58]. In addition, the three substrates demonstrate markedly
differing temperature dependencies in their kinetic isotope
effects. Scrutton and coworkers have described this enzyme
as one that demonstrates both promoting vibrations and the

overall importance of barrier shape rather than just barrier
height in biochemistry.
It seems then that there is a growing body of evidence that
protein dynamics could well play a central role in enzymatic
catalysis, well beyond standard pictures of loop motions
that cause substrate binding and change electrostatic
environments as substrates are transformed to products.
In fact, in cases where tunneling seems to play a significant
role, as indicated by kinetic isotope effect experiments,
directed motion of the protein could well be responsible for
a significant fraction of the catalytic mechanism. What is
lacking in the ongoing analysis, is a tool that allows,
through a knowledge of protein structure and an assump-
tion of a potential function for the protein, the rigorous
identification of the presence or absence of such a symmet-
rically coupled/promoting vibration. Such a theoretical
approach is especially important in light of the fact that
there is currently no general experimental method to detect
such a protein motion as it impacts catalysis. While
spectroscopic methods can, with extraordinary sensitivity,
interrogate localized motions in proteins, as we have
described above, the defining nature of a promoting
vibration is to be found in the nature of the coupling of
that motion to the reaction coordinate. There is no
experimental tool available to directly measure this coup-
ling. The next section details our theoretical approach to the
problem, and a recent application to alcohol dehydroge-
nase.
THE DETECTION OF PROMOTING
VIBRATIONS IN PROTEINS

The quantity that naturally describes the way in which an
environment interacts with a reaction coordinate in a
complex condensed phase is the spectral density. In Eqn (2),
the spectral density could be seen to give a distribution of
the frequencies of the bilinearly-coupled modes, convolved
with the strength of their coupling to the reaction coordi-
nate. The concept of the spectral density is, however, quite
general, and the spectral density may be measured or
computed for realistic systems in which the coupling of the
modes may well not be bilinear [61]. We have also shown
[18] that the spectral density can be evaluated along a
reaction coordinate. One only obtains a constant value for
the spectral density when the coupling between the reaction
coordinate and the environment is in fact bilinear. We have
shown that a promoting vibration is created as a result of a
symmetric coupling of a vibrational mode to the reaction
coordinate and, as described previously, this is quite a
general feature of motions in complex systems. Analytic
calculations demonstrated that such a mode should be
manifest by a strong peak in the spectral density when it was
evaluated at positions removed from the exact transition
state position, in particular in the reactant or product wells.
In cases where there is no promoting vibration, while the
spectral density may well change shape as a function of
reaction coordinate position, there will be no formation of
such strong peaks. Numerical experiments completed in our
group have shown a delta function at the frequency position
of the promoting vibration as the analytic theory predicted
when we study a model problem in which a vibration is
coupled symmetrically. The results of such calculations are

shown in Figs 3 and 4 [62]. These are spectral densities
calculated for the proton in a potential for proton transfer
between two carbon centers immersed in argon; shown in
Fig. 3 at the transition state, and in Fig. 4 with the proton at
a position near the reactant well. A more stringent test of the
approach is to be found in a similar computation when,
rather than explicitly including a symmetrically coupled
vibration, we simply create a system in which proton
transfer occurs between two vibrating atoms of a complex.
There we expect to find a promoting vibration, but the
identity of this vibration is not manifest in the model form,
rather it is buried in the dynamics of the atomic motions. In
fact, when we compute the spectral density for such a
proton transfer system with the proton held in the reactant
well and the effective mass of the vibrating system equal to
100 amu, we obtain the result shown in Fig. 5. Given the
0
50
100
150
200
250
300
0
5e-05
0.0001
0.00015
0.0002
0.00025
J(ω)

Fig. 4. The spectral density for the same system as in Fig. 3, but now
measured in the reactant well.
0
50
100
150
200
0
1e-05
2e-05
3e-05
4e-05
5e-05
J(ω)
Fig. 3. A spectral density for proton transfer between two carbon centers
with a symmetrically coupled vibration measured exactly at the transition
state – the point of minimum coupling.
3108 D. Antoniou et al. (Eur. J. Biochem. 269) Ó FEBS 2002
success of the methodology to detect the presence of a
promoting vibration in test calculations, the next goal is to
apply the methodology to a real enzyme system. The choice
we made was from the alcohol dehydrogenase family.
Our previous studies of alcohol dehydrogenase
enzymes involved yeast alcohol dehydrogenase (YADH)
and a mutant of alcohol dehydrogenase from Bacillus
stereothermophilus. YADH is advantageous for the study
of kinetic isotope effects and enzyme dynamics, because
the chemical step is rate determining and commitment
factors need not be found. We began our studies of
promoting vibrations in enzymes with HLADH [63] for

two reasons: first, there is as yet no crystal structure for
YADH, and such a structure is needed as a starting
point for any dynamics study of a protein. Second, there
are a number of mutants of HLADH, which allow
detailed study of the influence of protein composition on
protein dynamics, and how dynamics relates to kinetics
of catalysis.
Our analysis began with the 2.1-A
˚
crystal structure of
Plapp and coworkers [64]. This crystal structure contains
both NAD
+
and 2,3,4,5,6-pentafluorobenzyl alcohol com-
plexed with the native HLADH (metal ions and both the
substrate and cofactor.) The fluorinated alcohol does not
react and go onto products because of the strong electron
withdrawing tendencies of the flourines on the phenyl ring,
and so it is hypothesized that the crystal structure
corresponds to a stable approximation of the Michaelis
complex. We then replaced the fluorinated alcohol with the
unfluorinated compound to obtain the reactive species as in
Luo et al. [56]. This structure was used as input into the
CHARMM
program [65]. Both crystallographic waters [64]
(there are 12 buried waters in each subunit) and environ-
mental waters were included via the TIP3P potential [66].
The substrates were created from the
MSI/
charmm param-

eters. The NAD cofactor was modeled using the force field
of Mackerell et al. [67]. The lengths of all bonds to hydrogen
atoms were held fixed using the
SHAKE
algorithm. A time
step of 1 fs was employed. The initial structure was
minimized using a steepest descent algorithm for 1000 steps
followed by an adapted basis Newton–Raphson minimiza-
tion of 8000 steps. The dynamics protocol was heating for
5 ps followed by equilibration for 8 ps, followed finally by
data collection for the next 50 ps. Using
CHARMM
,we
computed the force autocorrelation function on the reacting
particle. The force is calculated in
CHARMM
as a derivative
of the velocity. This is a numerical procedure that can, of
course, introduce error. We have recently found that
spectral densities may also be calculated from the velocity
autocorrelation function directly, and these spectral densi-
ties exhibit exactly the same diagnostics for the presence of a
promoting vibration, as do those calculated from the force.
In addition, the Fourier transform of the force autocorre-
lation function can be shown to be related to the Fourier
transform of the velocity autocorrelation function times a
square of the frequency. This square of the frequency tends
to accentuate high frequencies. In a simple liquid, this is not
a problem because there are essentially no high frequency
modes. In a bonded system, such as an enzyme, many high

frequency modes remain manifest in autocorrelation func-
tions, and it is advantageous to employ spectral densities
calculated from Fourier transforms of the velocity function.
We will not have an ÔexactÕ reaction coordinate at our
disposal, but this does not affect the calculation. The
diagnostic of the promoting vibration is simply the presence
of a strong variation in the spectral density as the reacting
particle (in this case the hydride) is moved from the reactant
well to the product well. As long as it is moved on a vector
that contains some component of the reaction coordinate, a
sharp spike will appear in the spectral density at a frequency
corresponding to the promoting vibration, possibly shifted
by a small amount [63]. Thus, appearance of a strong peak
in the spectral density along the line connecting the
alcoholate and the NAD
+
should be found close to the
actual frequency of the promoting vibration. We then
calculated the force or velocity autocorrelation function on
the transferring particle, i.e. the hydride. A search through
position space in the vicinity of the transition state will yield
spectral densities in which a peak moves to ever-smaller
frequencies. The result with the smallest frequency should
be very close to the bare frequency of the promoting
vibration, and incidentally would locate the transition state
in the enzymatic environment. If the hypothesized promo-
ting vibration is present, we can immediately check the
frequency to ascertain if the predicted frequency is similar to
the frequency of motion of an expected residue, which is in
the putative protein motion. For example, a position

correlation function on Val203 should yield an oscillatory
function with period of oscillation close to that found in the
spectral density calculation, if in fact the hypothesis that this
residue is involved in a correlated motion that creates a
promoting vibration is correct. As a final first test of our
approach to the study of promoting vibrations in enzymes,
we subjected the Val203 fi Ala mutant to the same
computational procedure. Recall that this mutant has a
smaller side chain impinging on the face of the NAD
+
distal
to the alcohol. It is motion of this 203 residue into the
cofactor, pushing the cofactor ring system closer to the
alcohol, which is hypothesized to result in the creation of the
promoting vibration. With a smaller sidechain, we expect
Ôless of a pushÕ, which will be made manifest in a weaker
coupling of the promoting vibration to the reaction
coordinate. In turn this weaker coupling would appear in
0 100 200 300 400
500
ω (cm
-1
)
0
0.1
0.2
0.3
0.4
0.5
J(ω)

Fig. 5. The spectral density in the reactant well for a similar model, but
with no manifestly symmetrically coupled promoting vibration. In this
case the carbon centers move toward each other, and their motion
creates a promoting vibration similar to the benzoic acid system shown
in Fig. 1.
Ó FEBS 2002 Barrier passage and protein dynamics (Eur. J. Biochem. 269) 3109
our computations as a smaller peak in the spectral density at
positions remote from the transition state.
The results from these calculations are shown in Figs 6, 7,
and 8, with the spectral density now indicated by G(x),
showing that we compute this spectral density from a
velocity autocorrelation function rather than a force auto-
correlation function. We now employ a velocity autocorre-
lation function for a purely technical reason. In a simple
fluid, relatively slow frequency motions dominate all envi-
ronmental modes. Note for example, the first peak in Fig. 3
occurs at about 50 cm
)1
, and the spectral density is
essentially zero by 200 cm
)1
. In a protein, there are
vibrational modes extending up to CH stretches in the
thousands of wavenumbers. It can be shown that the
relationship between the force and the velocity autocorre-
lation functions is simply multiplication by the square of the
frequency. Thus in the force autocorrelation function, even
very weakly coupled modes, can be dominant when their
frequency is very high. When the methodology is applied to
the enzyme, we find exactly the expected results. First, Fig. 6

shows the spectral density for the hydride when held at the
reactant well, the product well and the transition state. We
find strong peaks in the spectral density for the reactant and
product configuration, with the spectral density for the
transition state configuration appearing flat. We note that
the results of the transition state computation are not zero;
they simply are so much lower in magnitude, than the results
at the reactants or products that they appear to be zero. In
fact the spectral density at the transition state is exactly of the
shape one would expect for the spectral density for a protein,
and this result is shown alone in Fig. 7. This is what was
found in Figs 3, 4 and 5. In addition, the spectral density for
the hydride held at the transition state in the Val203 fi Ala
mutant is exactly as was expected, i.e. similar frequency
peaks at lower intensity. It is interesting to note that in
locating the transition state location, defined in this instance
as the position of minimum coupling of the promoting
vibration to the reaction coordinate, we found that this
location differs slightly between the wild-type and mutant
enzymes. This is a further indication that protein dynamics
play a central role in the catalytic effect in these systems.
CONCLUSIONS
In this review, we have described work pursued in our group
over the past 5 years demonstrating the potential for protein
involvement in catalysis, and theoretical methods that
confirm the importance of such motions. These results have
relied heavily on experimental results from the laboratories
of the two other groups contributing reviews to this volume.
Our initial involvement in this area came as a result of trying
to understand why, in both biological and nonbiological

systems, there seemed to be cases of significant involvement
of quantum tunneling without the expected high primary
kinetic isotope effect.
0 500 1000 1500 2000 2500 3000
ω (cm
1
)
0.0
10.0
20.0
30.0
G
S
(ω)
(MC)
Fig. 7. The spectral density computed at the point of minimal coupling in
Fig. 6, shown alone. Note that the spectral density is an order of
magnitude smaller at the point of minimal coupling than in the reac-
tant or product wells. This result is similar in this respect to the result
obtainedinFigs3and4.
0 500 1000 1500 2000 2500 3000
ω (cm
1
)
50.0
50.0
150.0
250.0
350.0
450.0

550.0
G
S
(ω)
(R)
(P)
(MC)
Fig. 6. The spectral densities for wildtype horse liver alcohol dehy-
drogenase computed with the hydride held in the reactant well (r), the
product well (p), and at the point of minimal coupling (mc).
0 100 200 300 400
500
ω (cm
-1
)
0
100
200
300
G
S
(ω)
Val 203 → Ala mutant
wild-type
Fig. 8. A comparison of the spectral densities at the points of minimal
coupling for the wildtype HLADH and for the mutant Val203 fi Ala.
The smaller residue in the 203 position in the mutant is less strongly
coupled to the reaction coordinate, hence the lower peaks. Note that
the point of minimal coupling occurs at slightly different locations in
the two proteins.

3110 D. Antoniou et al. (Eur. J. Biochem. 269) Ó FEBS 2002
Having understood this puzzle, it is important to mention
that new problems have arisen. The first and foremost is the
large timescale separation between the promoting vibration
and the chemical turnover of the enzyme systems involved.
The dominant peaks in the spectral densities indicate
motions on the 150-cm
)1
frequency scale. This corresponds
to sub-picosecond vibrations. Clearly, many cycles of the
promoting vibration must occur before it is effective in
helping to cause chemical turnover. This is, of course, not
without precedence; motions such as loop closures in
proteins often happen many times before catalysis occurs.
The generally accepted explanation is that such ineffective
motions are the result of incorrectly placed groups or
substrate in the enzyme active site. In many ways, this issue
corresponds to finding the actual Ôreaction coordinateÕ in
any condensed phase problem. For example, in a proton
transfer in a polar solvent, reaction is not actually limited by
movement of the proton, but actually by rearrangement of
the solvent around the moving charged particle. Thus, what
specific motions and placements of atoms within the enzyme
and substrates are needed for catalysis will be a subject of
significant concern for theoretical research.
A second question of almost philosophical import is the
extent to which evolution has utilized protein dynamics in
concert with quantum tunneling to craft enzymes. It should
certainly come as no surprise that tunneling is used in
catalysis. Evolution knows nothing about which equation,

Newton’s or Schrodinger’s, is needed to understand
dynamics. All that is needed is the creation of a path from
reactants to products. It is interesting to consider that the
coupling of tunneling with protein dynamics in the form of
promoting vibrations may have been used to create
exquisite sensors of chemical substrates. Because tunneling
is exponentially dependent on tunneling distance, small
changes in distance in a promoting vibration can distinguish
between different substrates. Now in the case of alcohol
dehydrogenases, the promoting vibration is created via
transmission of dynamics from the protein to the constant
cofactor. In other enzymes this might not be the case. In
particular, the large variation in rates and kinetic isotope
effects for different substrates found in aromatic amine
dehydrogenase makes this enzyme a candidate for just such
a sensor. Location of the actual promoting mode within the
enzyme will be the first step in resolution of this issue.
ACKNOWLEDGEMENTS
We gratefully acknowledge the support of this work by the Office of
Naval Research and the National Science Foundation.
REFERENCES
1. Bruice, T.C. & Benkovic, S.J. (2000) Chemical basis for enzyme
catalysis. Biochemistry 39, 6267–6274.
2. Warshel, A. (1988) Electrostatic origin of the catalytic power of
enzymes and the role of preorganized active sites. J. Biol. Chem.
273, 27035–27038.
3. Cleland, W.W., Frey, P.A. & Gerlt, J.A. (1998) The low barrier
hydrogen bond in enzymatic catalysis. J. Biol. Chem. 273, 25529–
25532.
4. Pauling, L. (1948) Nature of forces between large molecules of

biological interest. Nature 161, 707–709.
5. Schramm, V.L. (1999) Enzymatic transition state analysis and
transition-state analogues. Methods Enzymol. 308, 301–354.
6. Schowen, R.L. (1978) Transition States of Biochemical Processes.
Plenum Press, New York.
7. Jencks, W.P. (1975) Binding energy, specificity and enzymatic
catalysis, the circle effect Adv. Enzymol. 43, 219–310.
8. Wu, N., Mo, Y., Gao, J. & Pai, E.F. (2000) Electrostatic stress in
catalysis, structure and mechanism of the enzyme orotidine
monophosphate decarboxylase. Proc.NatlAcad.Sci.USA97,
2017–2022.
9. Warshel, A. (1978) Energetics of enzyme catalysis. Proc. Natl
Acad.Sci.USA75, 5250–5254.
10. Cannon, W.R. & Benkovic, S.J (1998) Solvation, reorganization
energy and biological catalysis. J. Biol. Chem. 273, 26257–25260.
11. Bruice, T.C. & Torres, R.A. (2000) The mechanism of phospho-
diester hydrolysis: near in-line attack conformations in the ham-
merhead ribozyme. J. Am. Chem. Soc. 122, 781–791.
12. Marcus, R.A. (1964) Chemical and electrochemical electron
transfer theory. Ann. Rev. Phys. Chem. 15, 155–181.
13. Babamov, V. & Marcus, R.A. (1981) Dynamics of hydrogen atom
and proton transfer reactions: symmetric case. J. Chem. Phys. 74,
1790.
14. Lau, E. & Bruice, T.C. (1998) The importance of correlated
motions in forming highly reactive near attack conformations in
catechol O-methyltransferase. J. Mol. Biol. 120, 12387–12394.
15. Torres, R.A., Schiott, B.S. & Bruice, T.C. (1999) Molecular
dynamics simulations of ground and transition states for the
hydride transfer from formate to NAD
+

in the active site of
formate dehydrogenase. J. Am. Chem. Soc. 121, 8164–8173.
16. Hu, Y., Yang, X., Yin, D.H., Mahadevan, J., Kuczera, K.,
Schowen, R.L. & Borchardt, R.T. (2001) Computational char-
acterization of substrate binding and catalysis in, S-adenosylho-
mocysteine hydrolase. Biochemistry 40, 15143–15152.
17. Antoniou, D., & Schwartz, S.D. (1999) A molecular dynamics
quantum kramers study of proton transfer in solution. J. Chem.
Phys. 110, 465–472.
18. Antoniou, D. & Schwartz, S.D. (1999) Quantum proton transfer
with spatially dependent friction: phenol-amine in methyl chloride.
J. Chem. Phys. 110, 7359–7364.
19. Straub, J.E., Borkovec, M. & Berne, B.J. (1988) Molecular
dynamics study of an isomerizing diatomic in a lennard-jones
fluid. J. Chem. Phys. 89, 4833.
20. Gertner, B.J., Wilson, K.R. & Hynes, J.T. (1988) Nonequilibrium
solvation effects on reaction rates for model SN2 reactions in
water. J. Chem. Phys. 90, 3537.
21. Cortes, E., West, B.J. & Lindenberg, K. (1985) On the generalized
langevin equation: classical and quantum mechanical. J. Chem.
Phys. 82, 2708–2717.
22. Zwanzig, R. (1973) The nonlinear generalized langevin equation.
J. Stat. Phys. 9,215.
23. Zwanzig, R. (2001) Nonequilibrium Statistical Mechanics. Oxford
University Press, Oxford.
24. Schwartz, S.D. (1994) Accurate quantum mechanics from high
order resumed operator expansions. J. Chem. Phys. 100, 8795–
8801.
25. Schwartz, S.D. (1994) Vibrational energy transfer from resumed
evolution operators. J. Chem. Phys. 101, 10436–10441.

26. Antoniou, D. & Schwartz, S.D. (1995) Vibrational energy transfer
in linear hydrocarbon chains: new quantum results. J. Chem. Phys.
103, 7277–7286.
27. Schwartz, S.D. (1996) The interaction representation and non-
adiabatic corrections to adiabatic evolution operators. J. Chem.
Phys. 104, 1394–1398.
28. Antoniou, D. & Schwartz, S.D. (1996) Nonadiabatic effects in a
method that combines classical and quantum mechanics. J. Chem.
Phys. 104, 3526–3530.
29. Schwartz, S.D. (1996) The interaction representation and non-
adiabatic corrections to adiabatic evolution operators II: nonlin-
ear quantum systems. J. Chem. Phys. 104, 7985–7987.
Ó FEBS 2002 Barrier passage and protein dynamics (Eur. J. Biochem. 269) 3111
30. Karmacharya, R., Antoniou, D. & Schwartz, S.D. (2001) None-
quilibrium solvation, and the quantum kramers problem: proton
transfer in aqueous glycine. J. Phys. Chem. B105, 2563–2567.
31. Borgis, D. & Hynes, J.T. (1996) Curve Crossing Formulation for
Proton Transfer Reactions in Solution. J. Chem. Phys. 100, 1118.
32. Antoniou, D. & Schwartz, S.D. (1997) Large kinetic isotope effects
in enzymatic proton transfer, and the role of substrate oscillations.
Proc. Natl Acad. Sci. USA 94, 12360–12365.
33. Fuke, K. & Kaya, K. (1989) Dynamics of double proton transfer
reactions in the excited state model of hydrogen bonded base pairs.
J. Phys. Chem. 93,614.
34. Brougham, D.F., Horsewill, A.J., Ikram, A., Ibberson, R.M.,
McDonald, P.J. & Pinter-Krainer, M. (1996) The correlation
between hydrogen bond tunneling dynamics, and the structure of
benzoic acid dimers. J. Chem. Phys. 105,979.
35. Meier, B.H., Graf, F. & Ernst, R.R. (1982) Structure, and
dynamics of intramolecular hydrogen bonds in carboxylic acid

dimers: a solid state NMR study. J. Chem. Phys. 76, 767.
36. Stockli, A., Meier, B.H., Kreis, R., Meyer, R. & Ernst, R.R. (1990)
Hydrogen bond dynamics in isotopically substituted benzoic acid
dimers. J. Chem. Phys. 93, 1502.
37. Neumann, M., Brougham, D.F., McGloin, C.J., Johnson, M.R.,
Horsewill, A.J., Trommsdorff, H.P. (1998) Proton tunneling in
benzoic acid crystals at intermediate temperatures: nuclear mag-
netic resonance and neutron scattering studies. J. Chem. Phys. 109,
7300.
38. Antoniou, D. & Schwartz, S.D. (1998) Activated chemistry in the
presence of a strongly symmetrically coupled vibration. J. Chem.
Phys. 108, 3620–3625.
39. Antoniou, D. & Schwartz S.D. (1998) Proton transfer in benzoic
acid crystals: another look using quantum operator theory.
J. Chem. Phys. 109, 2287–2293.
40. Benderskii, V.A., Grebenshchikov, S. Yu & Milnikov, G.V. (1995)
Tunneling splittings in model, 2D potentials I. Chem. Phys. 194,1.
41. Benderskii, V.A., Grebenshchikov, S. Yu & Milnikov, G.V. (1995)
Tunneling splittings in model, 2D potentials III. generalization to
Ndimensionalcase.Chem. Phys. 198, 281.
42. Benderskii, V.A., Goldanskii, V.I. & Makarov, D.E. (1991) Low-
temperature chemical reactions. effect of symmetrically coupled
vibrations in collinear exchange reactions. Chem. Phys. 154,407.
43. Huskey, P. & Schowen, R. (1983) Reaction coordinate tunneling
in hydride-transfer reactions. J. Am. Chem. Soc. 105, 5704–5706.
44. Bell, R.P. (1980) The Tunnel Effect in Chemistry. Chapman &
Hall, New York.
45. Agarwal, P.K., Webb, S.P. & Hammes-Schiffer, S. (2000) Com-
putational studies of the mechanism for proton and hydride
transfer in liver alcohol dehydrogenase. J. Am. Chem. Soc. 122,

4803–4812.
46. Kohen, A., Cannio, R., Bartolucci, S. & Klinman, J.P. (1999)
Enzyme dynamics and hydrogen tunneling in a thermophilic
alcohol dehydrogenase. Nature 399, 496–499.
47. Cha, Y., Murray, C.J. & Klinman, J.P. (1989) Hydrogen tunneling
in enzyme reactions. Science 243, 1325.
48. Grant, K.L. & Klinman, J.P. (1989) Evidence that both protium
and deuterium undergo significant tunneling in the reaction cat-
alyzed by bovine serum amine oxidase. Biochemistry 28, 6597.
49. Kohen, A. & Klinman, J.P. (1998) Enzyme catalysis: beyond
classical paradigms. Accounts Chem. Res. 31,397.
50. Bahnson, B.J. & Klinman J.P. (1995) Hydrogen tunneling in
enzyme catalysis. Methods Enzymol 249, 373.
51. Rucker, J., Cha, Y., Jonsson, T., Grant, K.L. & Klinman, J.P.
(1992) Role of internal thermodynamics in determining hydrogen
tunneling in enzyme-catalyzed hydrogen transfer reactions. Bio-
chemistry 31, 11489.
52. Kohen, A., Klinman J.P. (2000) Protein flexibility correlates with
degree of hydrogen tunneling in thermophilic, and mesophilic
alcohol dehydrogenases. JACS 122, 10738–10739.
53. Zavodsky, P., Kardos, J., Svingor, A. & Petsko, G.A. (1998)
Adjustment of conformational flexibility is a key event in the
thermal adaptation of proteins. Proc. Natl Acad. Sci. USA 95,
7406–7411.
54. Bahnson, B.J., Colby, T.D., Chin, J.K., Goldstein, B.M. &
Klinman, J.P. (1997) A link between protein structure, A. and
enzyme catalyzed hydrogen tunneling. Proc.NatlAcad.Sci.USA
94, 12797–12802.
55. Bahnson,B.J.,Park,D H.,Kim,K.,Plapp,B.V.&Klinman,J.P.
(1993) Unmasking of hydrogen tunneling in the horse liver alcohol

dehydrogenase reaction by site-directed mutagenesis. Biochemistry
32, 5503–5507.
56. Luo, J., Kahn, K. & Bruice, T.C. (1999) The linear dependence of
for reduction of NAD
+
by PhCH
2
OH on the distance between
reactants when catalyzed by horse liver alcohol dehydrogenase
and 203 single point mutants. Bioorg. Chem. 27, 289–296.
57. Tsai, S C. & Klinman, J.P. (2001) Probes of Hydrogen tunneling
with horse liver alcohol dehydrogenase at subzero temperatures.
Biochemistry 40, 2303–2311.
58. Basran, J., Patel, S., Sutcliff, M.J. & Scrutton, N.S. (2001)
Importance of barrier shape in enzyme catalyzed reactions. J. Biol.
Chem. 276, 6234–6242.
59. Basran, J., Sutcliff, M.J., Scrutton, N.S (1999) Enzymatic
H-transfer requires vibration driven extreme tunneling. Biochem-
istry 38, 3218–3222.
60. Antoniou, D. & Schwartz, S.D. (2001) Internal enzyme motions
as a source of catalytic activity: rate promoting vibrations and
hydrogen tunneling. J. Phys. Chem. B105, 5553–5558.
61. Passino, S.A., Nagasawa, Y. & Fleming, G.R. (1997) Three pulse
stimulated photon echo experiments as a probe of polar solvation
dynamics: utility of harmonic bath modes. J. Chem. Phys. 107,
6094.
62. Caratzoulas, S. & Schwartz, S.D. (2001) A computational
method to discover the existence of promoting vibrations for
chemical reactions in condensed phases. J. Chem. Phys. 114, 2910–
2918.

63. Caratzoulas, S., Mincer, J. & Schwartz, S.D. (2002) Identification
of a protein promoting vibration in the reaction catalyzed by horse
liver alcohol dehydrogenase. JACS, 124, 3270–3276.
64. Ramaswamy, S., Elkund, H. & Plapp, B.V. (1994) Structures of
horse liver alcohol dehydrogenase complexed with, NAD
+
and
substituted benzyl alcohols. Biochemistry 33, 5230–5237.
65. Brooks,B.R.,Bruccoleri,R.E.,Olafson,B.D.,States,D.J.,Swa-
minathan, S. & Karplus, M. (1983) CHARMM, a program for
macromolecular energy, minimization, dynamics calculations.
J. Comp. Chem. 4, 187–217.
66. Jorgensen, W. Chandrasekher, J., Madura, J.D., Impey, R.W. &
Klein, M.L. (1983) Comparison of simple potential functions for
simulating liquid water. J. Chem. Phys. 79, 926.
67. Pavelites, J.J., Gao, J., Bash, P.A., Alexander, D. & Mackerell, J.
(1997) A molecular mechanics force field for NAD+ NADH and
the pyrophosphate groups of nucleotides. J. Comput. Chem. 18,
221–239.
3112 D. Antoniou et al. (Eur. J. Biochem. 269) Ó FEBS 2002