Enzyme Mechanisms: Fast Reaction and Computational Approaches
Probing coupled motions in enzymatic hydrogen
tunnelling reactions
Rudolf K. Allemann1 , Rhiannon M. Evans and E. Joel Loveridge
School of Chemistry, Cardiff University, Park Place, Cardiff CF10 3AT, U.K.
Abstract
Much work has gone into understanding the physical basis of the enormous catalytic power of enzymes over
the last 50 years or so. Nevertheless, the detailed mechanism used by Nature’s catalysts to speed chemical
transformations remains elusive. DHFR (dihydrofolate reductase) has served as a paradigm to study the
relationship between the structure, function and dynamics of enzymatic transformations. A complex reaction
cascade, which involves rearrangements and movements of loops and domains of the enzyme, is used to
orientate cofactor and substrate in a reactive configuration from which hydride is transferred by quantum
mechanical tunnelling. In the present paper, we review results from experiments that probe the influence
of protein dynamics on the chemical step of the reaction catalysed by TmDHFR (DHFR from Thermotoga
maritima). This enzyme appears to have evolved an optimal structure that can maintain a catalytically
competent conformation under extreme conditions.
Introduction
The enormous catalytic power of enzymes, which can achieve
rate enhancements of up to 21 orders of magnitude relative
to the uncatalysed reactions, has fascinated scientists for
many decades but has long remained mysterious. To a first
approximation, Koshland’s induced fit hypothesis [1], which
was built on the simple lock and key model proposed more
than a century ago by Emil Fischer [2], and its subsequent
adaptation to ground-state destabilization by Haldane [3],
is still applicable for describing the specificity and selectively
of enzymes. Enzymatic rate accelerations, on the other hand,
are generally explained by a lowering of the transition-state
energy and/or an increase of the ground-state energy in
a static energy barrier. This model, derived from Eyring’s
transition-state theory [4,5], has underpinned the design
of transition-state analogues for enzyme inhibition and the
creation of catalytic antibodies. More recently, however, it has
become increasingly clear that repositioning of the relative
energies of the ground and transition states along a static
energy barrier does not provide a sufficiently full explanation
of enzyme catalysis, and the role of quantum mechanical
tunnelling by protein dynamics (in addition to contributions
from zero-point energies) has become established, at least for
enzymes that transfer particles of relatively low mass such
as electrons or hydrogen atoms. In several enzyme systems,
it has been proposed that protein dynamics are coupled
to tunnelling, and a variety of models for active promotion of
tunnelling have been invoked, including rate-promoting vibrations [6–10], environmentally coupled tunnelling [11–13],
Key words: dihydrofolate reductase (DHFR), hydrogen tunnelling reaction, quantum mechanical
tunnelling, protein-coupled motion, protein dynamics, Thermotoga maritima.
Abbreviations used: DHFR, dihydrofolate reductase; EcDHFR, DHFR from Escherichia coli; KIE,
kinetic isotope effect; QM/MM, quantum mechanics/molecular mechanics; TmDHFR, DHFR from
Thermotoga maritima.
1
To whom correspondence should be addressed (email [email protected]).
Biochem. Soc. Trans. (2009) 37, 349–353; doi:10.1042/BST0370349
vibrationally enhanced ground-state tunnelling [14,15] and
multidimensional tunnelling [16,17].
The ubiquitous enzyme DHFR (dihydrofolate reductase),
which catalyses the conversion of 7,8-dihydrofolate into
5,6,7,8-tetrahydrofolate using NADPH as a cofactor, has
served as a paradigm for the development of a fundamental
understanding of enzyme catalysis through study of the
relationship between enzyme structure, dynamics and
catalysis of hydrogen-transfer reactions (transfer of H+ ,
H− or H• ). Owing to the central role of the enzyme in
maintaining intracellular pools of tetrahydrofolate, which
acts as a one-carbon carrier during the biosynthesis of
purines, thymidylate and several amino acids, DHFR
has long been recognized as a target for anticancer and
antibacterial drugs. DHFRs from more than 30 organisms
from the three domains of life have been characterized.
Kinetic measurements have revealed that hydrogen transfer
during catalysis by EcDHFR (DHFR from Escherichia
coli) occurred with a strong contribution from tunnelling promoted by dynamic motions of the protein [18,19].
Genomic sequence analysis combined with QM/MM
(quantum mechanics/molecular mechanics) simulations
identified an enzyme-wide network of hydrogen bonds and
van der Waals interactions in EcDHFR that was suggested to
influence protein dynamics and promote catalysis [20–27].
TmDHFR (DHFR from Thermotoga maritima) is the
most thermostable DHFR isolated. Its melting temperature
of 83◦ C is approx. 30◦ C above that of the E. coli enzyme
[28,29]. Despite only 27 % sequence identity, the T. maritima
and the E. coli DHFRs adopt similar tertiary structures
[30,31], although in contrast with all other chromosomally
encoded DHFRs that have been characterized,
TmDHFR forms a dimer that appears to be largely responsible for its increased thermal stability (Figure 1) [31,32].
Folding of TmDHFR was shown to be a two-state process
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Figure 1 Structural basis of thermal stability of TmDHFR
(A) Cartoon of the structures of monomeric EcDHFR (PDB code 1DRE
[30]) and dimeric TmDHFR (PDB code 1D1G [31]). NADPH and the substrate analogue methotrexate (MTX) are shown as sticks. (B) The dimer
interface of TmDHFR. Residues mentioned in the text are shown as sticks
and are indicated for one subunit.
identified, suggesting that dimerization might be important
not only for the thermal stability of TmDHFR but also for
its catalytic activity. Here, we report experiments that probe
the effects of solvent composition and dimerization on the
catalytic activity of TmDHFR.
Effects of dielectrics and viscosity
on TmDHFR catalysis
between unfolded monomers and the folded dimer; under no
experimental circumstances was a folded monomer observed
[32]. Interestingly, in addition to an extensive hydrophobic
core in the centre of the dimer interface, intersubunit
hydrogen bonds between the ends of β-strands βF and
βG confer significant stabilization on the dimer. If the
mobility of the βF–βG loop is also important in TmDHFR
catalysis, as had been suggested for the E. coli enzyme,
these interactions might also influence the rate of hydrogen
transfer in TmDHFR.
The rates of the hydride transfer reaction catalysed by
TmDHFR as a function of temperature were determined
by combined QM/MM calculations using EA-VTST/MT
(ensemble-averaged variational transition state theory with
multidimensional tunnelling) [33–35]. The behaviour of the
native TmDHFR dimer was compared with that of the experimentally inaccessible TmDHFR monomer. The results
suggest that quantum mechanical tunnelling makes a significant contribution to the reaction rate at all temperatures.
In addition, intra- and inter-subunit molecular motions were
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Authors Journal compilation Increasing the viscosity and decreasing the dielectric constant
of the reaction medium are both known to generally reduce
motions within a protein. Computational studies have shown
that while increased solvent viscosity affects the protein
interior just as much as the surface [36], decreasing the dielectric constant produces a pronounced reduction in motion
at the surface but the interior remains highly mobile [37].
Reducing the solvent dielectric constant inhibits motion by
strengthening the H-bonding network, which also increases
the protein’s stability [38]. It has also been suggested that
increased stability is accompanied by a decrease in flexibility
[38], although this view has recently been challenged through
results obtained in neutron scattering experiments [39].
Given this information, it has recently been proposed that
enzymes such as DHFR, in which tunnelling appears to be
coupled to long-range protein motions, could be affected
by changes to the solvent composition [40]. We recently
embarked on a study to test this proposal with TmDHFR,
using a range of organic co-solvents [41]. Our study revealed
no directly proportional effect from the solvent viscosity on
either the steady-state rate (kcat ) or the rate of hydride transfer
(kH ). Both rate constants, however, were decreased in a manner proportional to the dielectric constant, with the exception
of kH in the presence of glycerol (Figure 2). Bulk solvent properties had no significant effect on the KIE (kinetic isotope
effect) on either rate constant. CD spectroscopy indicated
that neither the secondary structure of TmDHFR nor its thermostability was significantly altered over the range in which
kinetics were measured. In combination with computational
results, which show that the dimer interface resists thermodenaturation longer than other regions of the enzyme [42], these
CD experiments provide strong evidence that dimerization of
TmDHFR is not disrupted by the co-solvents used.
The effect of solvent viscosity on the rate of enzymatic
reactions may be described by a theoretical model initially
developed by Kramers for unimolecular reactions [43]. A later
extension of this model predicts that enzymatic reaction rates
decrease with increasing solvent viscosity in a manner dependent on internal protein friction [44]. Molecular dynamics
studies of TmDHFR revealed intramolecular correlated
motions similar to those seen in EcDHFR as well as motions
correlated across the subunits of the TmDHFR dimer [45].
These results and Kramers theory predict a dependence of the
hydride transfer rates for the TmDHFR catalysed reaction on
solvent viscosity. However, our observed rate constants do
not fit the predicted dependence on solvent viscosity at any
value of the enzyme internal friction, showing that contrary to
expectations, solution viscosity does not affect the kinetics of
Enzyme Mechanisms: Fast Reaction and Computational Approaches
Figure 2 Plots of k H and k cat against solution viscosity (left) and
dielectric constant (right) at 20◦ C
The colours of the symbol indicate the different co-solvents (dark green:
no co-solvent; light green: tetrahydrofuran; yellow: sucrose; orange:
glycerol; red: ethylene glycol; maroon: propan-2-ol; dark blue: ethanol;
Figure 3 KIEs for TmDHFR-catalysed hydride/deuteride transfer
on a logarithmic scale against the inverse temperature in the presence of various concentrations of (A) methanol, (B) glycerol and
(C) sucrose
Data taken from [41].
and light blue: methanol). In the case of the data for the dielectric
constant, lines of best fits are shown. A separate line of best fit is shown
for the rate constants of hydride transfer, k H , as a function of glycerol
concentration. Data taken from [41].
TmDHFR. The dielectric constant of the solvent, however,
had a strong effect on both kH and kcat , although not on
their KIEs. It is most likely that the effect on TmDHFR is
due to inhibition of motions critical for catalysis, rather than
electrostatic effects on the reaction itself. The absence of an
effect from the viscoelastic response of the solvent supports
the view that TmDHFR motions are of low amplitude and
that this contributes to the low rates of reaction [28,45].
Increasing the concentration of glycerol (and sucrose) led
to increased rate constants for hydride transfer, suggesting
that these changes were compound specific and not a
consequence of changes to the bulk solvent properties. We
therefore measured the temperature dependence of the KIEs
for the chemical step in the presence of methanol, glycerol and
sucrose in the range 6–50◦ C (Figure 3). Above 25◦ C, the kinetic breakpoint observed in the absence of co-solvents, the addition of methanol had no effect on the KIE. Below 25◦ C the
KIEs became obscured by kinetic complexity, and no further
analysis was performed. In contrast, glycerol led to a reduction of both the KIE in the temperature-independent range,
and the temperature of the kinetic breakpoint. The range in
which KIEs were temperature-independent, i.e. in which preorganizational (‘passive’) dynamics dominate, was therefore
increased, while below the breakpoint the temperature dependence (determined by the difference in activation energies
for H− and D− transfer) was increased. Therefore glycerol
increases the reliance on ‘gating’ motions at low temperatures,
but reduces the range over which these motions dominate.
The effect of sucrose was slightly different from that of
glycerol. Although sucrose also reduced the KIE, it did not
do so in such an obviously concentration-dependent manner
as observed for glycerol, and furthermore the KIEs became
temperature independent over the entire experimental range.
The equivalent methanol and glycerol solutions used in
our study have very similar dielectric constants, whereas
the sucrose solutions used were isoviscous to the glycerol
solutions. The change in behaviour of the KIEs in the
presence of glycerol and sucrose is therefore clearly not
dominated by either the viscosity or the dielectric constant
of the reaction medium, and must instead be due to specific
effects from the two compounds. We speculate that these,
and presumably other, polyols may bind to the surface of
TmDHFR and disrupt certain interactions, for example by
exerting a loosening effect on the edges of the interface,
allowing increased motion of the loop regions and an increase
in the rate of hydride transfer. Alternatively, polyols may
have an effect on the layer of hydration water on the protein
surface, and so alter motions ‘slaved’ [46] to this layer.
Is the quaternary structure of TmDHFR
important for its catalytic efficiency?
TmDHFR is the most stable DHFR isolated so far. Its
stability is dependent both on an optimized composition
of the subunits and its dimeric structure [31,32]. Such is
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the stability of the dimer that no structured monomers
could be detected experimentally in equilibrium or during
unfolding [32]. Molecular dynamics simulations of the
thermal unfolding of TmDHFR revealed that folding of
the TmDHFR subunits and dimerization are intimately
linked and not stepwise processes in which folded monomers
associate to form the native dimer [42]. A central feature
of the dimer interface is a large hydrophobic core that is
flanked by intersubunit salt bridges and hydrogen bonds. The
mobility of certain residues involved in the dimer interface of
TmDHFR has been suggested to be important for catalysis
in monomeric DHFRs [47–49].
To address whether the rigidity resulting from dimerization may be responsible for the lower reaction rates observed
in TmDHFR when compared with mesophilic enzymes, specific amino acid replacements were introduced into the dimer
interface to increase the concentration of folded monomer
at equilibrium (Figure 1). Single or double mutations of
Glu136 and Glu138 to lysine residues to disrupt the main
intersubunit salt bridge did not affect dimerization. Similarly,
replacement of Val126 , located towards the edge of the central
hydrophobic patch next to the more hydrophilic periphery,
with a glutamate residue also had little effect. Preliminary data
indicate, however, that the replacement of Val11 , a residue that
is positioned more towards the centre of the hydrophobic
core of the interface, with aspartate destabilized the dimer
interface sufficiently to favour the monomeric form of the
enzyme (E.J. Loveridge, R. Rodriguez, R.S. Swanwick and
R.K. Allemann, unpublished work). The thermostability of
the monomer was reduced relative to the dimer, supporting the hypothesis that oligomerization is required to
achieve the necessary high thermal stability of TmDHFR. In
contrast, hydride transfer was not significantly impaired by
monomerization and hence the reduced rates of the chemical
step relative to EcDHFR are not a consequence of the dimeric
structure of TmDHFR. Dimerization is, however, clearly
crucial to allow the enzyme to maintain a stably folded
structure at the high temperatures at which its host survives
in the biosphere. In addition, the steady-state rates are
somewhat lower in the mutant, suggesting that intersubunit
motions may also influence the physical steps during the
reaction cycle of TmDHFR.
Conclusions
The results described here suggest that protein motions
during DHFR catalysis are important not only for the
physical steps but also for the actual hydride transfer.
Interestingly and against expectation based on molecular
modelling studies [36], a clear correlation between solvent
viscosity and reaction rates was not identified, but solventspecific effects are nevertheless transmitted to the active site of
TmDHFR. The preliminary data reported on a ‘monomeric’
version of TmDHFR suggest that ‘rigidity’ resulting from
dimerization is not the cause of the reduced catalytic activity
of TmDHFR when compared with the monomeric E. coli
enzyme. The chemical reaction in TmDHFR appears to have
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changes, perhaps through a protein scaffold that can tolerate
motions of higher amplitude than mesophilic DHFRs. In
this sense, TmDHFR may be the more flexible enzyme
better suited to accommodate larger fluctuations at increased
temperatures [39] while at the same time maintaining a
catalytically optimized active site.
Funding
This work was supported by the Biotechnology and Biological
Sciences Research Council [grant number BB/E008380/1].
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Received 6 October 2008
doi:10.1042/BST0370349
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