(Received for publication, April 10, 1995; and in revised form, January 22, 1996)
From the
A major challenge for theoretical simulation methods is the calculation of enzymic reaction rates directly from the three-dimensional protein structure together with some idea of the chemical reaction mechanism. Here, we report the evaluation of a complete free energy profile for all the elementary steps of the triosephosphate isomerase catalyzed reaction using such an approach. The results are compatible with available experimental data and also suggest which of the possible reaction intermediates is kinetically observable. In addition to previously identified catalytic residues, the simulations show that a crystallographically observed active site water molecule plays an important role during catalysis and an intersubunit interaction that could explain the low activity of the monomeric enzyme is also observed. The calculations clearly demonstrate the important catalytic effects associated with stabilization of charged high energy intermediates and reduction of reorganization energy, which are likely to be general principles of enzyme catalyzed charge transfer and separation reactions.
A wealth of enzymological (1, 2, 3, 4) and structural (5, 6) information has been obtained over the years
for the triose phosphate isomerase (TIM) ()catalyzed
reaction, and investigations of the uncatalyzed interconversion between
dihydroxyacetone phosphate (DHAP) and glyceraldehyde 3-phosphate (GAP)
have also been reported(7) . The current view of the functional
mechanism of the enzyme that has emerged from these studies can be
summarized as follows (see Fig. 1). (i) After binding of DHAP
one of the C-1 protons (1-pro-R) is abstracted by the
catalytic base Glu
, yielding a corresponding enediolate
species. (ii) This enediolate is then protonated at O-2 by the neutral
imidazole ring of His
, giving a doubly protonated enediol
and an imidazolate anion. (iii) His
recaptures a proton
from the O-1 oxygen again yielding an enediolate species, now lacking
the proton at O-1. (iv) Protonation of this enediolate at C-2 by the
carboxyl group of Glu
, thus restoring the general base to
give the product D-GAP, which then is released from the
enzyme. TIM is a fast enzyme that is limited by product release at
physiological substrate and product concentrations and with internal
rate constants on the order of 10
s
(3, 7) . As a comparison the
rate-limiting step for nonenzymatic conversion of DHAP is about
10
s
, in which case the mechanism
involves intramolecular proton abstraction by the phosphate
group(7) .
Figure 1:
The
catalytic mechanism of TIM is represented as a four-step process
(excluding binding and release steps). Five VB configurations
(-
) are used to describe the
reaction.
There are, however, still several open questions regarding the detailed mechanism that require an answer before we could claim a complete understanding of this enzyme. All of the proposed elementary steps cannot be discerned experimentally, and one instead observes only one kinetic intermediate state, but its exact nature is not known. The peculiar use of a neutral imidazole as proton donor has also attracted much attention (8, 9) and was actually a prediction from theoretical calculations of a rather unexpected result(9) . It has, however, recently been disputed in a study by Kollman and co-workers(10) . A number of other theoretical studies of TIM have been reported earlier dealing with amino acid mutations (11) and conformational changes (12) as well as quantum and molecular mechanics calculations on the catalytic reaction(13) .
Here, we report the calculation of a complete free energy profile for the proposed ``imidazolate'' reaction mechanism(4, 6, 9) using molecular dynamics (MD) free energy perturbation (FEP) simulations in combination with the empirical valence bond (EVB) method (14, 15) . Because some controversy regarding the detailed mechanism of TIM still exists, our goal here is to try to evaluate the energetics implied by the seemingly favored one in order to examine its feasibility. The x-ray coordinates of the yeast enzyme in complex with the inhibitor phosphoglycolohydroxamate (6) were used as the starting point. This inhibitor closely resembles one of the proposed (high energy) intermediates of the reaction, and no major modelling is required to construct the different reaction species (cf.Fig. 1) from it.
The TIM reaction is described here by the EVB model(14, 15) . This model treats the reaction (or rather each reaction step) as a conversion between different valence bond (VB) states or resonance structures. Each of these pure states is modelled by a molecular mechanics force field, whereas intervening configurations are obtained by mixing of the VB states. The EVB method has the advantage that it is easily incorporated into an MD framework where the reaction path can be mapped out by the FEP procedure. Furthermore, as will be discussed below, the method allows calibration against known experimental data because the VB states have a clear physical meaning. Accordingly, thermodynamic data for model reactions in water can be used to fine tune the EVB reaction surface(15) .
In the present case, the reaction path is
described by the five bonding configurations or resonance structures
depicted in Fig. 1. Each of these diabatic states
(-
) is represented by an
analytical force field of the standard molecular mechanics
type(16, 17) . In the cases where standard force field
parameters(16) , viz. partial charges, are not
available, they were derived from AM1/PM3 calculations using the AMSOL
program (18) and merged with the GROMOS group parameters in
order to achieve consistency with them. Fig. 2. shows the charge
distributions that were used for the substrate in each of the five VB
states. The parameters for dipolar groups of the substrate are very
close to the standard GROMOS ones. This is, of course, no guarantee
that they are correct unless the corresponding solvation free energies
have actually been verified(19) . However, for dipolar groups
the absolute values of the solvation energies are small, and the
corresponding errors will likewise be small. Moreover, there is clearly
some cancellation of errors inherent in the fact that we here only
consider the difference between solution and enzyme. For
charged groups, on the other hand, solvation energies are large, and
the nonbonded parameters are more crucial for energetics. Therefore we
have employed parameters for the negatively charged oxygens that have
been carefully calibrated earlier against hydration free
energies(17) . The other van der Waals' parameters (16) pertaining to charged groups (e.g. for N and P)
have also been checked. (
)We are thus rather confident that
the energetics associated with the present force field(s) is
reasonable, and it should perhaps again be emphasized that (i) we only
examine the difference between water and enzyme and (ii) the total free
energy difference between different EVB resonance structures is
calibrated to match experimental solution data prior to carrying out
the enzyme calculations (see below). Bonds within the reacting
fragments (defined as the depicted atoms in Fig. 1) were
represented by Morse potentials using standard values for bond lengths
and dissociation energies(20) . The
CH
OPO
moiety was, however,
represented with the standard harmonic bond functions (16) because these bonds are not broken during the reaction.
Figure 2:
Partial atomic charges used in the
calculations for the substrate in the various resonance forms. The
standard GROMOS van der Waals' parameters (16) were used
except for the oxygens bearing a large negative charge
(q
> 0.5) for which the parameters derived
in (17) were used (these have been calibrated to reproduce
hydration free energies for carboxylate
ions).
Although the force field(s) above can describe the interactions
between the fragments of each state and with the surrounding medium, as
well as the energies involved in distorting geometries from their
equilibrium, it does not contain information about the relative
energies of the fragments in vacuum. That is to say that there is an
energy difference, , between any two fragments that is related to
their heats of formation that is not included in the molecular
mechanics force field. Furthermore, standard force fields cannot
describe the quantum mechanical coupling between states reflected by
off-diagonal terms of the hamiltonian. The above information can,
however, be obtained either by quantum mechanical calculations or by
gas phase or solution experiments. The latter alternative, to use
experimental data to calibrate the above mentioned gas phase parameters
of the system hamiltonian (which we refer to as EVB parameters, cf.Table 1), is the essence of the EVB
method(14, 15) . In particular, it has proven useful
to calibrate the potential energy surface with respect to solution
experiments by simulating suitable reference reactions in water. The
parameters that are subject to this calibration are the above-mentioned
gas phase energy differences (
values) between the VB states and
the off-diagonal matrix elements H
(see below).
The former are mainly associated with reaction free energies, whereas
the latter mainly affect activation barriers. The resulting parameters
are then directly transferred to simulations of the corresponding
reaction steps in the solvated enzyme. The advantage with this approach
is that the energetics in an aqueous environment can be reproduced
exactly and one then ``only'' has to be able to model the substitution of water by protein (note, however, that the
choice of reference reactions corresponds to the assumed mechanism in the enzyme and not necessarily to that of the uncatalyzed
reaction, which may proceed by a different mechanism). The alternative
would be to rely on a (semi-empirical) molecular orbital model to
correctly reproduce the gas phase energetics and then
``substitute'' vacuum for the actual environment in the
enzyme by coupling to a molecular mechanics force field(9) .
This may involve more serious transferability problems, and the idea
with the EVB reference reaction calibration is thus to diminish these.
In the present case some of the data needed for calibration is not
directly available from experiment due to the ``high energy''
nature of the proposed intermediates, e.g. the solution
pK values of hydrogens on C-1 and C-2 as
well as the associated activation barriers. Starting from the
pK
of acetone in water of
19.2(21) , these pK
s can,
however, be estimated by the substituent effects of a hydroxyl group
and the phosphate dianion. The latter interaction, i.e. between the enediolate and phosphate anions, has been determined
to be about one pK unit in water (7) . In order to
estimate the additional effect of a hydroxyl group on the
pK
of acetone, we carried out
semi-empirical SCF calculations in a homogeneous dielectricum (
= 80) using the AMSOL program(18) . Calculations with
the AM1-SM2 and PM3-SM3 hamiltonians yield a pK
shift of -3.8 and -5.4 pK-units, respectively.
Taking into account the observed effect of the phosphate group (7) and after correcting for the number of equivalent protons,
we arrive at a pK
value of 17.2 for
abstracting a C1 proton from DHAP, using the AM1-SM2 result, and 15.6
using the PM3-SM3 result. The former of these values seems most
reasonable in that it gives a free energy relationship that nicely fits
experimental data on acetone and DHAP deprotonation from independent
sources(7, 22) , as shown in Fig. 3(our
estimate of the pK
at 17.2 is also rather
close to the value inferred by Richard(7) ). The corresponding
pK
value of 15.9 for LGAP is related by
the observed equilibrium constant of to that of DHAP(7) . By
interpolation in the diagram, the free energy relationship of Fig. 3can also be used to deduce the activation barriers for
proton exchanges with the carboxylate moiety of glutamic acid in
aqueous solution (pK
= 4.1), which
are used as reference reactions for the first and fourth step of the
enzymic conversion (cf.Table 1). The second and third
steps of the enzyme reaction, according to the mechanism of Fig. 1, involve proton transfer between the substrate oxygens
and the imidazole ring of His
. The pK
difference between donor and acceptor in solution is about 2
pK units, with the neutral imidazole ionizing at the higher
pK
of 14 (9) and the enediol at
12(22) . The proton transfer barriers for these reference
reactions can, in the same way as above, be determined quite accurately
from a free energy relationship based on experimental data of Eigen and
co-workers (Table IV of (23) and Table V of (24) ),
and the corresponding energetics are listed in Table 1.
Figure 3:
Free
energy relationship (activation barrier versus pK
) comprising experimental
data on acetone deprotonation by various bases ((22) , squares) and on base catalyzed phosphate elimination reactions (7) of DHAP (circles) and LGAP (triangles)
using the estimated pK
values of DHAP and
LGAP. The latter pK
was related to the
former by the observed equilibrium constant of between LGAP and DHAP
in solution(7) . All values have been corrected for the number
of equivalent protons.
Hence,
the energetics of the four reaction steps as they would occur in
aqueous solution, assuming a nonconcerted imidazolate mechanism, can be
determined as described above, and the resulting free energy diagram is
shown in Fig. 4(curve a). Each of these steps is then
simulated in a separate MD calculation with the reacting fragments
immersed in a sphere of water. The FEP technique (25, 26, 27) is used to drive the system
between the five different VB configurations (Fig. 1) while
mapping out the free energy profile (potential of mean force along the
reaction coordinate) on the actual ground state potential surface by
the potential of mean force procedure that has been described
elsewhere(14, 15, 17) . The ground state
energy is obtained for any given configuration of the system (set of
coordinates) by mixing the VB states and solving the corresponding
secular equation (14, 15, 17) . These
simulations of the uncatalyzed reference reactions are used to obtain
values of the (unknown) gas phase free energy differences, ,
between the VB states and of the off-diagonal hamiltonian matrix
elements (the latter are represented by functions of the form
µ
=
A
e
Figure 4:
a, free energy diagram for the TIM
reaction mechanism in aqueous solution based on experimental data (7, 21, 22, 23, 24) and
semiempirical AMSOL (18) calculations. EVB/FEP/MD calibrations
of each of these steps in water were carried out so that the resulting
free energy profile reproduces the depicted energetics (14, 15) . b, free energy diagram for the
corresponding reaction steps in the enzyme. The transition states
associated with the four reaction steps are denoted -
. The top panel also shows the
detailed free energy profile for the first enzymic step with the
abscissa denoting the energy gap between the
and
diabatic states.
The simulation characteristics were the same as in (17) and (28) . For each step in water and in the protein, a 70-ps
trajectory was calculated using about 30 values of the FEP coupling
parameter , yielding a total simulation time of 560 ps excluding
equilibration. At each
-point the first 40% of the data was
discarded. The simulations were carried out at approximately 300 K with
an MD time step of 0.002 ps. Spherical systems of radius 15 Å
were used with the boundaries restrained by the SCAAS model (29) (water molecules) and by harmonic restraints to
crystallographic positions (protein atoms). The spheres were centered
on the C-1 carbon atom both in the protein and water simulations. The
substrate and charged protein groups interacted with everything within
the simulation sphere, whereas cut-offs as specified in (28) were applied to other interactions. The convergence error
bars obtained by forwards and backwards integration of the same
trajectories were examined and found to range between 0.5 and 1.5
kcal/mol. In addition, some extra runs with different initial
conditions were also carried out to try to assess the accuracy of the
results, and these gave very similar error ranges. Although the above
values give an estimate of the MD convergence errors (per reaction
step), it should be noted that an equally important source of error for
the resulting enzyme energetics is the accuracy of the solution data
used for calibration. These errors are unfortunately more difficult to
estimate because they are determined by the accuracy of the
pK
values for the different species as well as the
free energy relationships used to extract barrier heights ( Fig. 3and Refs. 23, 24).
The resulting free energy profile from the EVB/FEP/MD
calculations is summarized in the diagram of Fig. 4(curve
b). The large catalytic effect of enzyme is evident, and it can be
seen that all three intermediates along with their flanking transition
states are stabilized relative to the reactant and product by some 15
kcal/mol compared with the uncatalyzed reactions. Of the four
intervening free energy barriers, one finds that those associated with
proton transfer to and from the substrate carbons limit the (internal)
rate of conversion. The simulations place both and
at lower energy than the doubly protonated species,
with
as the most stable intermediate along the path.
This would thus be the main contributor to the experimentally observed
kinetic intermediate and corresponds to the case with O-1 protonated.
For direct comparison with experimental results, Table 2lists
the rates calculated from the transition state theory equation using a
transmission factor of unity assuming that
is the
only kinetically significant (observable) intermediate. The calculated
free energy profile thus appears to be in reasonable agreement with
available kinetic data(3, 7) . Both the magnitude of
the kinetically significant internal activation barriers (12.5
kcal/mol) and the corresponding equilibrium constants are fairly close
to the experimental estimates. The theoretical calculations thus
reproduce the catalytic effect of the enzyme remarkably well, within
the accuracy limits that we can estimate (see above).
The origin of
the catalytic power of TIM has been the subject of much
discussion(4, 6, 9, 10, 11) .
We find here that there are two general effects at work: (i) stabilization of charged intermediates and (ii) reduction
of reorganization energy. Although both of these effects cause a
lowering of activation barriers, it is appropriate to distinguish them
from each other because the ``mechanism'' by which the
barriers are reduced are fundamentally different in the two cases. In
the first case, the transition states flanking an intermediate are
lowered as a consequence of the stabilization of that intermediate (Fig. 5B). This is basically the rationale behind
so-called linear free energy relationships, such as the Hammond
postulate, where one observes a systematic dependence of G
on
G
for a series of similar
reactions. The second effect, on the other hand, corresponds to a
``pure'' transition state stabilization that does not affect
G
for the given reaction step (Fig. 5C). The intervening barrier between two states
is instead lowered as a consequence of a reduced energy gap between the
potential surfaces of these states. In the terminology of electron
transfer theory(30) , the reorganization energy (
) for a
diabatic reaction is defined as the (absolute) free energy change that
would be measured on the product potential surface if the geometry, or
reaction coordinate, of the system is changed from the reactant surface
minimum to the product minimum (Fig. 5). For adiabatic reactions, such as the proton transfers considered here, the
reorganization energy can still be defined in terms of the diabatic
surfaces, although the barrier height is not solely determined by the
intersection of these but also by the magnitude of the off-diagonal
matrix elements(31) . That is to say that the quantum
mechanical coupling between the states causes a lowering of the
activation barrier compared with the diabatic case where this coupling
is zero.
Figure 5:
Schematic representation of the two
observed sources of catalysis. A, uncatalyzed reaction. B, catalysis by reaction energy reduction (e.g. stabilization of intermediates). C, catalysis by
reorganization energy reduction. The two solid curves in each
diagram are the diabatic reactant and product free energy surfaces, and
the dashed curve represents the adiabatic ground state
surface. The reorganization energy is denoted by
.
The first of the above effects favors the transfer of
negative charge from Glu to the substrate as well as
His
. The proximity of Lys
(which also forms
an ion pair with Glu
) to the substrate together with
hydrogen bonds from His
and Asn
are found to
be important for the stability of the enediolate species, in agreement
with earlier conjectures(6, 9) . Lodi and Knowles (32) have also pointed out the presence of the ``well
aimed''
-helix directed at His
that presumably
contributes to the stability of the imidazolate ion. Furthermore, the
present simulations indicate that an active site water molecule,
located approximately between Glu
and His
(denoted 626 in the PDB entry 7tim), plays an important role
during catalysis (Fig. 6). This water has sufficient rotational
and translational freedom so as to follow the ``negative
charge'' because it is translocated within the active site, and it
can provide stabilization by hydrogen bonding to Glu
, the
substrate, and His
when these are negatively charged. In
fact, the H-bonding network in the active site appears to be
particularly well suited for adaptation to the movement of
negative charge during catalysis.
Figure 6:
Stereo snapshot of the TIM active site in
the intermediate state () with His
negatively charged. The water molecule corresponding to number
626 in the PDB entry 7tim can be seen between His
and
Glu
. Other water molecules in the active site and dipolar
NH groups of the protein solvating the phosphate anion are also
shown.
Based on the above observation
regarding the role of water one would expect that a
mutation that displaces this water molecule should hamper catalysis.
Judging from the structure mutations of Ser
,
Cys
, or Ile
might cause such an effect.
Interestingly, we note that Blacklow and Knowles (33) have
examined the S96P mutant and found that it considerably reduces the
catalytic efficiency. This mutant would indeed appear to displace
water
, and our results suggest that this could be the
reason for its reduced activity. Furthermore, we observe that the
hydroxyl group of Thr
of the second subunit can
interact with the deprotonated histidine in the
intermediate state (Fig. 6). As in the crystal structure,
Thr
donates a hydrogen bond to the carboxylate group of
Glu
when His
is neutral, but in the second
reaction step the hydrogen bond can switch to the negative imidazolate
ring of His
, thereby providing additional stabilization of
this group. This behavior could thus provide a new clue to the low
enzymatic activity of monomeric TIM (34) , because Thr
belongs to the second subunit. Borchert et al.(34) have shown by protein engineering of trypanosomal TIM
that a shortening of the loop around Thr
(involving
deletion of this residue) yields a stable monomeric enzyme. This TIM
variant still retains most of its substrate affinity (20-fold lower for
LGAP than the wild type) while having a 1000-fold lower value of k
(34) . Thr
(from the
second subunit) has also been implicated as an important residue in the
work by Brown and Kollman(35) , for a somewhat different
reason. These authors carried out a 5 ps MD simulation of monomeric TIM
in vacuum and found considerable disruptions of the active site as a
result.
Our simulations show that the mechanism proposed by Bash et al.(9) involving the imidazolate species is
energetically and structurally very reasonable. The distinction between
this mechanism and that proposed by Alagona et
al.(10, 13) , which involves intramolecular proton transfer between the substrate oxygens, is, however, rather
subtle. The difference only pertains to whether a proton is relayed via
His or whether the -NH dipole on this residue merely
provides a hydrogen bond during intramolecular transfer. The barrier
obtained by Alagona et al.(13) in vacuum for this
process is only about 14 kcal/mol, and more recent calculations
including protein residues within 10 Å of the substrate and a
realistic model of DHAP yielded a barrier of about 12
kcal/mol(10) . One can thus not exclude the possibility that
the enzyme also could function via such an intramolecular process. A
possible problem with this alternative, however, is that the His
dipole would seem to interact less favorably with the
intramolecular transition state than with the enolates. Comparing Fig.
11 (c and d) of (10) also suggests that this
is the case, because the barrier increases by some 5 kcal/mol when
His
(plus all other residues within 10 Å of the
substrate) are included as opposed to the calculation with only
Asn
, Lys
, Ser
, and Glu
present(10) .
In the present work we find that the
barriers for the intermolecular mechanism are low enough not to be rate
determining. This is in contrast with (9) and (10) where they are too high to be compatible with experiment.
It should also be noted here that these studies did not calculate room
temperature free energies but rather minimum energy paths at zero
temperature, which may involve more serious problems with local minima.
Furthermore, in Ref.10 water molecules do not appear to have been
included, which could lead to exaggerated electrostatic effects. In our
simulations we also find that the pK difference between imidazole and the enediol is not altered
very much by the enzymic environment. However, in both the work of
Alagona et al.(10) and that of Bash et
al.(9) , the proton transfer from imidazole is
considerably ``uphill.'' This might seem a bit awkward in
view of the experimental finding that the (first) pK
of His
is significantly lowered in
enzyme(8) . Alagona et al.(10) further argue
that the fact that the nearby lysine residue (Lys
)
normally has a lower pK
than imidazole
would disfavor His
as a proton donor. This may, however,
be of less relevance because (i) the pK
of His
is known to be lowered(8) , as
mentioned above, and (ii) Lys
participates in a salt
bridge with Glu
, which presumably raises its
pK
value. Regarding the issue of inter- versus intramolecular proton transfer pathways, it has also
been shown that the mutant enzyme with His
replaced by
Gln, rather than to employ intramolecular proton transfer, uses
Glu
to effect all the proton tranfers(36) .
However, we can of course not make any judgement of the energetics of
the intramolecular process on the basis of the calculations reported
here. On the other hand, our simulations suggest that the proton
transfer barriers of the imidazole mechanism are at least low enough to
not limit the rate of the enzyme.
The ability to reduce
reorganization energies seems to be an important property of
enzymes(15, 37) . For a given chemical reaction step,
part of the energy barrier can be viewed as an intrinsic contribution
that does not depend on G
(the reaction free
energy) but on the curvature of the free energy functions of the
reactant and product states, which reflects the reorganization, e.g. of dipolar groups, involved in the reaction(30) .
In the case of large energy gaps between the reactant and product
surfaces at their respective minima, there will thus be a considerable
reorganization of the system as the reaction proceeds, which gives rise
to the intrinsic barrier. This is typically the case for charge
separation and transfer reactions in aqueous solution, where water
molecules must change their average polarization direction. In enzymes,
polar groups are attached to a relatively rigid framework and are
therefore less reorientable than in water. This fact, together with a
clever design of the framework in which dipoles are pointing in a
favorable direction, can lead to a considerable reduction of the
reorganization energy compared with solution reactions. In the present
calculations we observe this effect in all the steps of the
catalyzed reaction. Fig. 7compares the diabatic free energy
curves (i.e. the free energy curves of the pure VB states
without considering their mixing) in water and in the enzyme for the
states
and
, corresponding to the
second reaction step. These free energy curves are obtained by the same
potential of mean force formulation as that used to calculate the
ground state profile(31) . The reorganization energy upon going
from
to
can be defined as
=
-
G
, where
=
-
is the energy gap
between the two curves at the minimum of
. Vice
versa,
=
-
G
for the opposite
reaction,
now being measured at the minimum of
. In the case of the second reaction step, the
absolute value of
G
is small (about 3
kcal/mol both in solution and enzyme), and the reduction of
reorganization energy can therefore be seen directly from the fact that
the energy gaps at the minima of the diabatic ``reactant''
and ``product'' free energy surfaces for the reaction step
are clearly smaller in the enzyme than in solution. In this case, as
can be seen from Fig. 4, which gives the actual adiabatic energies (i.e. the ground state free energy surface after
mixing the VB states), the enzyme leaves
G
close to its uncatalyzed value and mainly affects the barrier
height.
Figure 7:
Diabatic free energy functions for the
states and
in water (upper
curve) and in the enzyme (lower curve) as a function of
the energy gap between the two states. The reorganization energies (see
text for definition) upon transfer from the reactant to the product
state and vice versa for this (the second) reaction step are indicated.
The reduction of reorganization energy in the protein is reflected by
the energy gaps being significantly smaller than in the uncatalyzed
reaction.
Another convincing proof of the reorganization energy
reduction effect can be obtained by artificially adjusting
G
(by varying the gas phase energy difference
discussed above) for a given reaction step in water so that it
coincides with the calculated value in the enzyme and then compare the
resulting hypothetical barrier height with that in the enzyme. For the
first step, one then obtains a barrier of 17.3 kcal/mol in water with
the same reaction free energy as in the protein. The fact that the
barrier obtained in this way is considerably higher than in the protein
shows that the enzyme indeed does more than simply change relative
pK
s (the same conclusion is reached for
the other steps as well). The stabilization of transition states can
thus be achieved both by lowering the energies of
intermediates and by reduction of the above-mentioned energy gaps or
reorganization energies. One can, in principle, imagine several ways of
achieving the latter, but at least when the reaction involves polar
states it is clear that a protein matrix with properly oriented dipoles
(or electric fields) can provide a microenvironment that responds with
a smaller reorganization than water while still providing a substantial
solvation of polar states. It is interesting to note here that the
possibility of reorganization energy reduction as a source of catalysis
in enzymes was conjectured already in 1980 by Albery(38) .
In view of the observations above it is interesting to try to
examine Menger's recently proposed ``split-site model''
with which he has attempted to rationalize the catalytic effect of TIM without invoking TS stabilization(39) . Menger instead
suggests that binding energy at a site (viz. the phosphate
group) at some distance from the reaction centre is used to destabilize
the reactant ground state by forcing the substrate into a conformation
characterized by unfavorable ``compressive and desolvation
forces'' that raise the reactant energy level and accelerate the
reaction (see also the review by Page (40) and references
therein). In our simulations we find no evidence of substrate
compression or strain, the average intramolecular substrate energies
being very similar in water and in the protein. As far as the
desolvation idea is concerned, its implication here is a possible
destabilization (upwards pK shift) of the
negatively charged Glu
upon substrate binding. There is
no doubt that the pK
difference between DHAP and the catalytic base is reduced by the enzyme (cf. Fig. 4) and to some extent the question of where
the absolute pK
s end up is of less
importance. We can, however, make the following observations. The
negatively charged intermediates of the reaction are clearly stabilized
by several hydrogen bonds, and their electrostatic interaction energy
with the surroundings is considerably more favorable than in water.
That the active site is biased toward negative charge is also evidenced
by the observed (8) pK
drop of
His
and by the strong binding of the phosphate group. A
comparison of the evironment around Glu
in the unliganded
enzyme (5) and the substrate reactant state (R) shows
an equal number of three hydrogen bonds to the carboxylate group (in
the latter case from the thiol group of Cys
, the DHAP
hydroxyl group, and a water molecule). Thus, the most obvious
explanation for the small reaction free energy differences of the first
and last steps is that there is large stabilization of the negatively
charged intermediates. This does not, of course, exclude the
possibility of the Glu
pK
being shifted somewhat upwards but the main effect does not
appear to be ``ground state destabilization.'' Instead, our
results clearly implicate the two effects mentioned above as
responsible for the catalytic power of TIM.
It should perhaps again be emphasized that the two general effects implicated here as the source of catalysis are not in any way at variance with the notion of transition state stabilization. Rather they constitute two different ways of achieving such a stabilization, and in that sense provides a clearer picture of what the enzyme does. It seems very likely to us that these two effects constitute general principles for enzymic catalysis of charge transfer and separation reactions. Certainly, more investigations are required to establish this point, but a considerable amount of data has accumulated during recent years that seem to support such a conjecture(14, 15, 17, 31, 37) .