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 unique role for the p
Trang 1M I N I R E V I E W
Barrier passage and protein dynamics in enzymatically catalyzed reactions
Dimitri Antoniou1, Stavros Caratzoulas1,*, C Kalyanaraman1, Joshua S Mincer1and Steven D Schwartz1,2
1
Department of Biophysics, Albert Einstein College of Medicine, Bronx, NY, USA;2Department 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; promotingvibration; promotingmode
I N T R O D U C T I O N
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 correspondingsolution phase reactions This
review will describe work recently completed in our group
that has focused on examiningthe 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 rate promotingvibrations, 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 maskingthe normal kinetic
indicators of such a phenomenon It is this feature that we
have proposed as a unifyingprinciple for some experimental
data relatingto tunnelingin 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 alongwith promotingvibra-tions Followingthis, 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 promotingvibrations 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 promotingvibration 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
P O T E N T I A L M O D E S O F E N Z Y M A T I C
A C T I O N
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 beingtransformed 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: sschwartz@aecom.yu.edu
Abbreviations: NAC, near attack conformations; HLADH, horse liver
alcohol dehydrogenase; YADH, yeast alcohol dehydrogenase.
Note: a website is available at http://www.aecom.yu.edu/home/sggd/
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)
Trang 2intermediate point thought to be at or near the top of the
solution phase (i.e uncatalyzed) barrier to reaction This
preferential bindingreleases 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 usingkinetic 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 duringthe 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 bindingand
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 makingthe
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; loweringthe 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 livingcells 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 near attack
conformations (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
reactingand formingproducts 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 loweringof the barrier is not statistical loweringof
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 tunnelingsystem (the probability to tunnel increases exponentially with a reduction of the width
of the tunnelingbarrier), 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
A N E N Z Y M E A S A C O N D E N S E D P H A S E :
T H E O R E T I C A L F O R M U L A T I O N F O R
T H E S T U D Y O F C H E M I C A L R E A C T I O N
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 havingtheir 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
Trang 3approach 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 pioneeringwork 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
(somethingthat 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 Quantum Kramers
methodology [17,18] Our ideas were motivated by the
followingapproximations 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 fluctuation-dissipation
the-orem, 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:
H¼ P
2
s
2ms
þ VoþX
k
P2k 2mk
þ1
2mkx
2
k qk cks
mkx2 k
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 is the strength of the coupling of the
environmental mode to the reaction coordinate, and mk and xkgive 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:
JðxÞ ¼p 2
X k
c2
mkxk dðx xkÞ dðx þ xkÞ
Here d(x) xk) is the Dirac delta 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 usingZwanzigHamiltonian, 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, usingmethods 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 followingingredients Given a potential for the enzymatic reaction, we model the exact problem usingZwanzig’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 molecular dynamics 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 couplingon reflection about the origin This property has deeper implications than the mathematical nature of the symmetry
Trang 4properties 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
m 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 tunnelingtheory,
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 bath plus coupling 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 tunnelingconfiguration
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
usingsuch an approach The reason for this is that the
antisymmetric couplingcontained within the Zwanzig
Hamiltonian does not physically represent all possible
important motions in a complex reactingsystem 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,
shown in Fig 1 Such systems had been studied for many
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:
H¼ P
2 S 2ms
þ VoþX
k
P2k 2mk
þ1
2mkx
2 qk cks
mkx2
þP
2 Q 2Mþ1
2mX
2 Q Cs
2
MX2
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 usingthis method and experimentally available param-eters for the benzoic acid proton transfer potential, we were able to reproduce experimental kinetics as longas 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 couplingcauses 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 alongany 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 tunnelingpath The action also includes the mass of the particle beingtransferred, and so in the symmetric couplingcase, 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 followingof a different physical path, even when tunnelingdominates,
Fig 1 A benzoic acid dimer The reaction coordinate in this case is the
symmetric transfer of the hydroxyl protons to the carbonyl oxygen.
The promotingvibration is the symmetric motion of the oxyg ens
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 usinga 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 kcalÆmol)1
D 5.21 3.14 3.01 kcalÆmol)1
Trang 5that 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 tunnelingadded (the Bell correction; [44]) and they
could not be used to account for enzymatic reactions in a
deep tunnelingregime
Klinman and coworkers have helped pioneer the study of
tunnelingin 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 bindingof 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 pKaof 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 tunnelingin the rate-determiningstep of hydride transfer Remarkably, their kinetic data seem to show that the thermophilic enzyme actually exhibits less signs of tunnelingat 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 determiningstep in catalysis for this enzyme Two specific mutations have been identified, Val203fi Ala and Phe93fi 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 bindingpocket 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, missingin 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 tunnelingis seen as the temperature is raised.)
A final set of enzymes now thought to exhibit dynamic protein control of tunnelinghydrogen transfer is that in the amine dehydrogenase family Scrutton and coworkers have extensively studied these enzymes [58] Though similarly named and havinga 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 determiningchemical 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 strongtemperature dependence in the measured activation energy This experimental data has been inter-preted as showingthat 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
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 modulatingthe one dimensional double
well potential (before couplingalongthe 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 alonga straig ht 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 corner cutting under the barrier For example, a
proton and a deuteron will follow different paths under the barrier.
Trang 6Another 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
differingtemperature dependencies in their kinetic isotope
effects Scrutton and coworkers have described this enzyme
as one that demonstrates both promotingvibrations 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 bindingand change electrostatic
environments as substrates are transformed to products
In fact, in cases where tunnelingseems 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
lackingin the ongoinganalysis, is a tool that allows,
through a knowledge of protein structure and an
assump-tion of a potential funcassump-tion for the protein, the rigorous
identification of the presence or absence of such a
symmet-rically coupled/promotingvibration 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 definingnature of a promoting
vibration is to be found in the nature of the couplingof
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
T H E D E T E C T I O N O F P R O M O T I N G
V I B R A T I O N S I N P R O T E I N S
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 couplingof the
modes may well not be bilinear [61] We have also shown
[18] that the spectral density can be evaluated alonga
reaction coordinate One only obtains a constant value for
the spectral density when the couplingbetween the reaction
coordinate and the environment is in fact bilinear We have
shown that a promotingvibration is created as a result of a
symmetric couplingof 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 strongpeak 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 promotingvibration, while the spectral density may well change shape as a function of reaction coordinate position, there will be no formation of such strongpeaks Numerical experiments completed in our group have shown a delta function at the frequency position
of the promotingvibration 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 includinga symmetrically coupled vibration, we simply create a system in which proton transfer occurs between two vibratingatoms of a complex There we expect to find a promotingvibration, 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 vibratingsystem equal to
100 amu, we obtain the result shown in Fig 5 Given the
0 5e-05 0.0001 0.00015 0.0002 0.00025
Fig 4 The spectral density for the same system as in Fig 3, but now measured in the reactant well.
0 1e-05 2e-05 3e-05 4e-05 5e-05
Fig 3 A spectral density for proton transfer between two carbon centers witha symmetrically coupled vibration measured exactly at the transition state – the point of minimum coupling.
Trang 7success of the methodology to detect the presence of a
promotingvibration 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 determiningand commitment
factors need not be found We began our studies of
promotingvibrations 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
withdrawingtendencies 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
CHARMMprogram [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 theMSI/charmm
param-eters The NAD cofactor was modeled usingthe force field
of Mackerell et al [67] The lengths of all bonds to hydrogen
atoms were held fixed usingtheSHAKEalgorithm A time
step of 1 fs was employed The initial structure was
minimized usinga steepest descent algorithm for 1000 steps
followed by an adapted basis Newton–Raphson minimiza-tion of 8000 steps The dynamics protocol was heatingfor
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 inCHARMMas 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 promotingvibration, 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 exact reaction coordinate at our disposal, but this does not affect the calculation The diagnostic of the promoting vibration is simply the presence
of a strongvariation in the spectral density as the reacting particle (in this case the hydride) is moved from the reactant well to the product well As longas 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 correspondingto the promotingvibration, possibly shifted
by a small amount [63] Thus, appearance of a strongpeak
in the spectral density alongthe line connectingthe alcoholate and the NAD+ should be found close to the actual frequency of the promotingvibration We then calculated the force or velocity autocorrelation function on the transferringparticle, 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-tingvibration 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 promotingvibration is correct As a final first test of our approach to the study of promotingvibrations in enzymes,
we subjected the Val203fi 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, pushingthe cofactor ringsystem closer to the alcohol, which is hypothesized to result in the creation of the promotingvibration With a smaller sidechain, we expect
less of a push, which will be made manifest in a weaker couplingof the promotingvibration to the reaction coordinate In turn this weaker couplingwould appear in
ω (cm -1
) 0
0.1
0.2
0.3
0.4
0.5
Fig 5 The spectral density in the reactant well for a similar model, but
withno manifestly symmetrically coupled promoting vibration In this
case the carbon centers move toward each other, and their motion
creates a promotingvibration similar to the benzoic acid system shown
in Fig 1.
Trang 8our 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),
showingthat 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 extendingup 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 strongpeaks 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 Val203fi Ala mutant is exactly as was expected, i.e similar frequency peaks at lower intensity It is interestingto note that in locatingthe transition state location, defined in this instance
as the position of minimum couplingof 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
C O N C L U S I O N S
In this review, we have described work pursued in our group over the past 5 years demonstratingthe 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 tunnelingwithout the expected high primary kinetic isotope effect
) 0.0
10.0
20.0
30.0
GS
(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
obtained in Fig s 3 and 4.
ω (cm 1
)
50.0
50.0
150.0
250.0
350.0
450.0
550.0
GS
(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).
ω (cm -1
) 0
100 200 300
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 couplingoccurs at slightly different locations in the two proteins.
Trang 9Havingunderstood 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)1frequency scale This corresponds
to sub-picosecond vibrations Clearly, many cycles of the
promotingvibration must occur before it is effective in
helpingto 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 findingthe actual reaction coordinate 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 movingcharged 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 tunnelingto craft enzymes It should
certainly come as no surprise that tunnelingis used in
catalysis Evolution knows nothingabout 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 interestingto consider that the
couplingof tunnelingwith protein dynamics in the form of
promotingvibrations may have been used to create
exquisite sensors of chemical substrates Because tunneling
is exponentially dependent on tunnelingdistance, 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 promotingmode within the
enzyme will be the first step in resolution of this issue
A C K N O W L E D G E M E N T S
We gratefully acknowledge the support of this work by the Office of
Naval Research and the National Science Foundation.
R E F E R E N C E S
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) Bindingenerg y, 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 Natl Acad Sci USA 97, 2017–2022.
9 Warshel, A (1978) Energetics of enzyme catalysis Proc Natl Acad Sci USA 75, 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 forminghighly 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 bindingand 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 isomerizingdiatomic 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 non-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 non-adiabatic evolution operators II: nonlin-ear quantum systems J Chem Phys 104, 7985–7987.
Trang 1030 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 tunnelingin
benzoic acid crystals at intermediate temperatures: nuclear
mag-netic resonance and neutron scatteringstudies 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 usingquantum operator theory.
J Chem Phys 109, 2287–2293.
40 Benderskii, V.A., Grebenshchikov, S Yu & Milnikov, G.V (1995)
Tunnelingsplittings in model, 2D potentials I Chem Phys 194, 1.
41 Benderskii, V.A., Grebenshchikov, S Yu & Milnikov, G.V (1995)
Tunnelingsplittings in model, 2D potentials III generalization to
N dimensional case 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 determininghydrogen tunnelingin 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 Natl Acad Sci USA
94, 12797–12802.
55 Bahnson, B.J., Park, D.-H., Kim, K., Plapp, B.V & Klinman, J.P (1993) Unmaskingof hydrogen tunnelingin 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 promotingvibrations 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 promotingvibrations 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 promotingvibration 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 simulatingliquid 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.