TIBS-779; No. of Pages 8
Review
A new understanding of how
temperature affects the catalytic
activity of enzymes
Roy M. Daniel1 and Michael J. Danson2
1
2
Thermophile Research Unit, Department of Biological Sciences, University of Waikato, Hamilton, New Zealand
Centre for Extremophile Research, Department of Biology and Biochemistry, University of Bath, Bath BA2 7AY, UK
The two established thermal properties of enzymes are
their activation energy and their thermal stability, but
experimental data do not match the expectations of
these two properties. The recently proposed Equilibrium
Model (EM) provides a quantitative explanation of
enzyme thermal behaviour under reaction conditions
by introducing an inactive (but not denatured) intermediate in rapid equilibrium with the active form. It
was formulated as a mathematical model, and fits the
known experimental data. Importantly, the EM gives rise
to a number of new insights into the molecular basis of
the temperature control of enzymes and their environmental adaptation and evolution, it is consistent with
active site properties, and it has fundamental implications for enzyme engineering and other areas of biotechnology.
The importance of understanding the effects of
temperature on enzymes
Enzymes catalyse nearly all chemical transformations
within cells, and it is therefore self-evident that an understanding of enzymes and the way in which they respond to
different conditions is fundamental not only to investigations of normal cellular functions, but also to the ability
to manipulate these functions through enzyme and metabolic engineering. Furthermore, any serious incursion into
systems biology is dependent on having available data on
enzyme concentrations, activities and regulatory responses
in the cell, organism or system in question.
An important feature in many of these cellular and
regulatory studies is how enzymes respond to changes in
temperature. The widely held classical view of the change
in enzyme activity with temperature (Box 1), namely an
exponential increase in reaction rate concomitant with a
decrease in the amount of active enzyme through irreversible thermal inactivation, was first seriously questioned by
Thomas and Scopes [1] while they were investigating the
effects of temperature on the kinetics and stability of
mesophilic and thermophilic 3-phosphoglycerate kinases.
In essence, when observing the change in enzyme activity
with temperature, they found that the decrease in kcat with
a rise in assay temperature above the temperature optiCorresponding author: Danson, M.J. ([email protected]).
This article is dedicated to our friend and colleague, Professor Robert
Eisenthal (1936–2007), who was one of the key architects of the
Equilibrium Model and contributed to all the work described in this paper.
mum of the enzyme was greater than might be expected
from irreversible thermal inactivation; reversible thermal
unfolding was suggested as one possible explanation. Similarly, our own studies revealed several cases in which the
activity of an enzyme at high temperatures was lower than
would be expected from its observed thermal stability, and
that some of this loss of activity above the temperature
optimum was indeed reversible [2–4]. From this work, we
concluded that thermal stability is necessary, but not
sufficient, for thermoactivity.
To account for these and other similar effects, we proposed an alternative model, the Equilibrium Model (EM),
which provides a more complete and quantitative description of the variation of enzyme activity with temperature
[5,6], and one that is applicable to all enzymes that have
been analysed [7]. The central feature of the model is the
introduction of a reversibly inactivated form of the enzyme;
this simple change not only allowed the development of a
model that now fits experimental data, but gives rise to a
Glossary
Eact: Catalytically active form of an enzyme; this encompasses all active species.
Eact = E0 Einact X. The EM assumes enzyme saturation and therefore Eact is
in effect ES, the enzyme–substrate complex.
Einact: Catalytically inactive, but not denatured, form of an enzyme that is in
reversible equilibrium with Eact. Einact thus encompasses all the totally inactive
species in rapid equilibrium with Eact, where ‘rapid’ means ‘faster than can be
detected using simple enzyme assays’.
[E0]: Total concentration of enzyme in an assay, comprising Eact, Einact and X
DG*cat: Gibbs’ free energy of activation for an enzyme-catalysed reaction.
DG*inact: Gibbs’ free energy of activation for the irreversible thermal inactivation of an enzyme.
h: Planck’s constant (6.626 1034 J.s)
DHeq: Change in enthalpy for the Eact to Einact transition.
kB: Boltzmann’s constant (1.381 1023 J/K)
kcat: Catalytic rate constant of an enzyme.
kinact: Rate constant for the irreversible thermal inactivation of an enzyme.
Keq: The equilibrium constant for the Eact Einact equilibrium.
KM: The Michaelis constant. Operationally, KM is the concentration of substrate
resulting in an enzyme achieving half its Vmax.
R: Gas constant (8.314 J/mol/K)
Teq: The temperature at which the Eact Einact equilibrium is at its mid-point
(Keq = 1). In the original publication of the EM [5], the term Tm was used for this
temperature, but Tm is now used exclusively for the melting temperature.
Tm: The melting temperature of a protein. In a two-state model of reversible
protein unfolding, Tm is the temperature at which the equilibrium between
folded and unfolded forms of the enzyme is at its mid-point.
Topt: The assay temperature at which the catalytic activity of an enzyme is at its
maximum value, under a defined set of assay conditions.
Vmax: The maximum velocity achievable by a given quantity of an enzyme.
Vmax = kcat [E0).
X: Irreversibly thermally inactivated form of an enzyme.
0968-0004/$ – see front matter ß 2010 Elsevier Ltd. All rights reserved. doi:10.1016/j.tibs.2010.05.001 Trends in Biochemical Sciences xx (2010) 1–8
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TIBS-779; No. of Pages 8
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Trends in Biochemical Sciences Vol.xxx No.x
number of unexpected insights. Thus, the model not only
contributes to a quantitative understanding of the role and
regulation of enzymes in cellular function, but also has
implications for diverse areas such as bioreactor design
and operation, enzyme engineering, and investigations
into how enzymes have evolved and adapted to changes
in environmental temperatures [8–11].
The Equilibrium Model
Compared with the textbook or ‘Classical’ Model (CM) [12–
14], the EM [5,6] describes an additional temperaturedependent component of enzyme activity, namely the
effect of temperature on the equilibrium position between
active (Eact) and inactive (Einact) forms of the enzyme (Box
1, Box 2). Therefore, although
V max ¼ kcat ½Eact where the dependence of kcat on temperature remains as
for the Classical Model, the concentration of active
enzyme at any time point is defined by:
½Eact ¼
½E0 ½X
1 þ K eq
where Keq is the equilibrium constant between active and
inactive forms of the enzyme, that is,
K eq ¼ ½Einact =½Eact The variation of enzymatic rate with temperature and
time during assay in the EM (Box 2, Figure Ia and b)
makes it obvious that, even when an initial rate is determined by measuring the increase in product concentration over short time periods and extrapolating the
rate back to time zero (t0), the enzyme shows a temperature optimum, confirming that enzyme activity is being
lost through a shift in the newly proposed Eact/Einact
equilibrium, because no significant denaturation can
have occurred at t0. Thus, a feature of the EM is that,
at temperatures above Teq, the initial (t0) rate decreases
(for example, Box 2, Figure Ia). Moreover, depending on
the value of Teq with respect to the temperatures at which
significant inactivation is observed during the time course
of the assay, there is a much smaller change in the
apparent temperature optimum with time in the EM than
in the CM [6]. In effect, the Eact/Einact reversible equilibration provides a ‘thermal buffer’ that protects the
enzyme from thermal inactivation. It is interesting to
Box 1. The CM and the EM: what is the difference?
The ‘Classical’ Model
The (Classical) model that can be found in many textbooks for the
effects of temperature on an enzyme is a two-state model, where Eact
! X(inactive); that is, an increase in temperature involves an increase in
catalytic activity, with the simultaneous decrease in the amount of
active enzyme through thermal irreversible inactivation [12–14]. The
variation in enzyme activity with temperature (T) and time (t) can
therefore be described by:
V max ¼ k cat ½E 0 e k inact t
Equation 1
The variation of the two rate constants with temperature is given
by:
k cat ¼
k B T DG cat
e RT
h
Where
K eq ¼ e
DH eq
R
1
1
T eq T
Equation 6
and the variation of kcat and kinact with temperature is given by
Equations 2 and 3, respectively. Teq is the temperature at which the
Eact/Einact equilibrium is at its mid-point (Keq = 1), and is equal to DHeq/
DSeq.
In this case, a plot of rate versus temperature versus time does have
an optimum for initial rates (that is, at t0) because of the assumption
that the Eact/Einact equilibration is rapid (Figure 1). Equation 5 can be
expanded [6] to:
Equation 2
and
k B T DG inact
Equation 3
e RT
h
In this case, a plot of temperature and rate against time has no
optimum for initial rates (that is, at t0) because denaturation is timedependent (Figure 1).
k inact ¼
The Equilibrium Model
The EM [5] introduces an intermediate inactive (but not denatured)
form of the enzyme that is in rapid equilibrium with the active form:
Equation 4
where Eact is the active form of the enzyme, which is in equilibrium
with the inactive form, Einact. Keq is the equilibrium constant
describing the ratio of Einact/Eact; kinact is the rate constant for the
Einact to X reaction; and X is the irreversibly inactivated form of the
enzyme. It should be noted that the equation is not intended to imply
that the conversion from Einact to X is a single step, or that X is a single
species, but only that they can be treated as such because all species
beyond Einact are irreversibly inactivated.
Using the EM, the variation of enzyme activity with temperature can
be expressed by:
k inact K eq t
V max ¼
2
k cat E0 e 1þK eq
1 þ K eq
Equation 5
The model describes the variation of V max with time and
temperature. It has the advantage of enabling the determination of
all four parameters (i.e., DG*cat, DG*inact, DHeq and Teq) simultaneously under reaction conditions (Box 2). However, it should be
noted that the term Eact (and possibly Einact) might be more correctly
denoted as ESact, in that the active enzyme will be saturated with
substrate to the degree expected under the conditions needed to
obtain Vmax.
It should also be noted that the EM delineates how enzyme
activity varies with temperature but, in itself, makes no prediction
or comments on how this variation is achieved. However, using
the Model does allow experimentation to address these issues
[16].
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Box 2. The EM: determination of parameters
Determination of the parameters for the EM requires generation of
enzyme progress curves (usually in triplicate) over a variety of
temperatures (Figure Ia), with at least two of the temperatures being
above Teq [33]. The data can then be fitted to Equation 7 to generate
the EM parameters; from these parameters, a 3D plot of rate,
temperature and time can be generated (Figure Ib) and compared
with the experimental data. A Matlab version of Equation 7 is
available at http://hdl.handle.net/10289/3791 to facilitate data fitting.
Given the exponential nature of the equation, it is evident that small
inaccuracies in the data can cause large errors. The Matlab program
generates fitting errors, and the website contains a number of other
measures to assess the fit of the data to the EM. In addition to these
fitting errors, the effect of experimental errors on the parameters
must be considered. Using continuous spectrophotometric assays,
we found that these errors are < 0.5% for the determination of Teq,
DG*cat and DG*inact, and <6% for the determination of DHeq [33].
However, in the case of stopped reactions, it could be difficult
to generate data with sufficient precision to obtain a good fit to
the EM. For full details, see ref [33] and http://hdl.handle.net/10289/
3791.
Figure I. Generation and analysis of experimental data for the EM. (a) The progress curves shown are for alkaline phosphatase, assayed at a variety of temperatures (K),
and are expressed as the concentration of product formed with time during the assay. A normal experiment requires triplicate assays at 10 temperatures; the number
of plots shown here has been reduced for clarity. The rate at any time point in the assay is given by the tangent to the curve (d[P]/dt) at that time point. Note the lower
initial rates above Teq (319K for this enzyme) leading to a t0 optimum temperature for activity in the 3D plot, characteristic of the EM. (b) The 3D experimental plot was
generated by fitting the raw data progress curves (a) to the model using a Matlab version of Equation 7 [http://hdl.handle.net/10289/3791]. Note that the Teq (319K) is
close to, but not necessarily coincident with, the graphical optimum [6,15].
note that this effect is seen even if the EM is generalized to
allow for the possibility of Eact also undergoing thermal
inactivation (Box 3, Scheme 2). The graphical optima
(Topt) found at t0 are not necessarily coincident with Teq
and are derived from a complex mixture of Teq, DG*cat,
DG*inact and DHeq [6,15].
Experimental data for all the enzymes we have studied
show an activity optimum at t0, consistent with the EM
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Box 3. Possible variants of the EM
If Einact is on the pathway to denaturation, which might be expected
if Einact is a marginally unfolded form of the enzyme, then the overall
pathway is likely to be as shown in Equation 4, that is:
Fast
slow
Eact Ð Einact !X
Scheme 1
This has the advantage of being a simple arrangement, in the
sense of minimal physical events/pathways being postulated,
although there could be several steps between Einact and the
irreversibly-inactivated form (X); for this reason we have described
the EM in these terms. However, there is an alternative. If Scheme 1
is extended to allow:
Slow
Fast
slow
X Eact Ð Einact !X
Scheme 2
so that both Eact and Einact lose activity irreversibly, with similar
rate constants, the rate/temperature/time profile looks much like
that found for the EM, although at lower temperatures Scheme 1 is a
better fit to the data. Generalizing the model in this way has the
disadvantage of introducing a second DG*inact parameter, to define
the new kinact (Eact ! X). In validating the model with real data [6–
8,16], we find that four parameters (i.e. without allowing Eact to
undergo irreversible inactivation) are sufficient to fit the EM to rate–
temperature–time data. By comparing possible variants of the EM, it
is apparent that for Scheme 2, direct conversion of Eact to X will be
relatively slow (A. D. Easter (2010), MSc Thesis, University of
Waikato, New Zealand).
In an extreme case of Scheme 2, irreversible inactivation might
proceed only from Eact, although this would mean that reversibly
inactivated enzyme (Einact) would need to be reactivated before
irreversible inactivation could occur, and would imply that the Einact
form is more stable than the native (active) form. However, the
speed of the Eact/Einact interconversion makes it difficult to
distinguish this possibility from Scheme 1.
The key element of the EM, that of a reversibly inactivated (single
or multiple) species in rapid equilibrium with the active enzyme is
common to all these possibilities and the EM as formulated
(Scheme 1) is sufficient to explain all the experimental observations.
(Figure 1). Notably, the CM shows no such optimum. More
than 50 datasets from more than 30 enzymes have been
examined, including enzymes from most reaction classes,
ranging from monomeric to hexameric structures and
including at least one enzyme in which the active site lies
at a subunit interface [16]. The EM is therefore apparently
universally applicable, and independent of the reaction
concerned and of enzyme structure. The original caution
[5] regarding the potentially limited application of the EM
now seems misplaced; however, we cannot exclude the
possibility that more complex models will fit the dependence of enzyme activity on temperature equally well.
Previous models for the effect of temperature on
enzymes
Several models have been proposed to account for the effect
of temperature on enzyme activity and stability, and it is
important to note their similarities to, and differences
from, the EM.
Time-independent changes in activity
Sizer [17] obtained parameters for the activation and
deactivation processes of catalase from the slopes of the
(approximately) linear portions of his plot of ln (rate)
against 1/T. He did not propose a model to account for
his observations, which were obtained from initial rates
and so were effectively at t0. Sizer’s analysis, as modelled
4
Figure 1. The temperature dependence of enzyme activity: experimental data
compared with simulations based on the CM and EM. The plots of rate (mM/s)
versus temperature (K) versus time (s) for Caldocellulosirupter saccharolyticus
ß-glucosidase illustrate the effect of temperature on enzymatic activity. The
experimental data plot is in red. The EM plot is derived by fitting the
experimental data to equation 7, to derive the four EM parameters for the
enzyme (DG*cat = 79 kJ/mol, DG*inact = 104 kJ/mol, Teq = 349 K and DHeq = 131 kJ/
mol). Re-inserting these values into the EM results in a simulated plot (blue) that
is a good match to the experimental data. The experimental data cannot be fitted
to the two-state CM, but if the values obtained for DG*cat and DG*inact are
inserted into the CM (green), there is no optimum at t0 (denaturation is timedependent).
by Cornish-Bowden [18] and by Bailey and Ollis [19], is
time-independent and only addresses the variation of the
observed catalytic rate constant with temperature, with
the total (potentially) active enzyme remaining constant;
that is, it does not include the possibility of time-dependent
irreversible inactivation.
Equilibrium between more than one active form
Keith Laidler’s text, The Chemical Kinetics of Enzyme
Action [20] also addresses the problem of enzyme deactivation and proposes several alternative mechanisms, one of
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Trends in Biochemical Sciences
which is based upon a study by Wright and Schomaker [21]
of the inactivation of diphtheria antitoxin by heat (and by
pH and urea), that bears some similarity to the EM. Wright
and Schomaker proposed the scheme
P Ð N ! I;
where P is a postulated active ‘protected’ antibody, N is the
native antibody and I is the irreversibly-inactivated antibody. Using an elegant kinetic analysis, these authors
showed that their model fitted their data, which were
effectively progress curves of inactivation. They made no
assumption of a rapid equilibrium, and treated the system
as one consisting of three first-order reactions. Their
method enabled them to obtain the rate constants for
the three steps of their model. They also recognised that
the model provided a reservoir of native antibody during a
significant fraction of the time course. However, although
their analysis allows total active protein (in their case,
antibody) to decrease with time, it assumes implicitly that
the ‘activity’ does not vary with temperature and that,
extrapolating from antibody to enzyme, both P and N
are active. The EM makes neither assumption, although
it does make the implicit assumption that the equilibrium
between Eact and Einact is rapid compared with the catalytic
reaction and the thermal denaturation.
Equilibrium between native and unfolded forms of the
enzyme
Lumry and Eyring [22] drew attention to the observation of
Hardy [23] that the first-order behaviour of irreversible
protein denaturation processes is often the result of the
overall process being limited by a preliminary reversible
step, in particular unfolding followed by aggregation. In the
EM, the Einact species is not unfolded significantly, and the
differences between Eact and Einact are associated with the
active site. It should also be noted that, under commonly
used assay conditions, it is extremely rare for the thermal
unfolding of an enzyme to be readily or rapidly reversible.
The localisation of the Eact–Einact interconversion
The EM does not in itself offer an explanation of the
molecular basis of the Eact–Einact interconversion, or the
physical nature of Einact. However, several lines of evidence
point to the interconversion being localised at the active
site of an enzyme and to Einact not being a significantly
unfolded form of the enzyme.
A plot of initial (t0) enzyme rates against temperature
has an optimum, implying that above this optimum,
increased temperature causes activity loss (by conversion
of Eact to Einact) faster than the initial rate can be
measured. Therefore, the assumption of the EM that the
Eact/Einact equilibration is very rapid [5] is evidently valid.
From the 3D plots of rate versus time versus temperature
Vol.xxx No.x
(Box 2, Figure Ib; Figure 3), the decline of activity with
time at a particular temperature gives the rate of denaturation at that temperature, and these values show that
the rate of denaturation is very much slower than the rate
of conversion of Eact to Einact. In addition, DHeq values for
enzymes are smaller than their corresponding DHunfold by
about an order of magnitude[16]. Both of these observations show that if Einact is unfolded, it can be only to a
very limited extent. Furthermore, it is possible, using
dilute denaturing agents, to change the stability of an
enzyme without affecting its Teq or DHeq [10]. Data from
circular dichroism (CD) experiments provide direct evidence that the Eact–Einact transition occurs very rapidly
compared with denaturation, is temperature-dependent,
and is physically distinct from the slower denaturation
process [16]. It is clear that Einact does not meet the criteria
expected for a molten globule state [24].
A variety of data has shown that the Teq and DHeq
values for a given enzyme are substrate and/or cofactor
specific, and that Teq and DHeq can change without an
effect on DG*inact and vice versa [16]. For example, in
considering subtilisin and its substrates Succ-AAPLpNA and Succ-AAPNle-pNA (where the only difference
between the two substrates is that norleucine has replaced
leucine), the values for DG*cat and DG*inact are essentially
the same, but the values for DHeq and Teq are significantly
different (Table 1). Similarly, the values of DHeq and Teq for
b-glucosidase are significantly different for para-nitrophenyl (pNP)-fucose (a 6-deoxyhexose sugar) and pNP-xylose
(a pentose sugar), although in this case, DG*cat and
DG*inact are also different.
Furthermore, reductive cleavage of a disulfide bond at
an active site [16] and preliminary data from site-directed
mutagenesis studies show that single amino changes at an
active site can also change Teq and DHeq without necessarily affecting DG*inact. Another indication of the nature of
Einact is that sharp changes of KM with temperature [25]
often coincide with Teq, consistent with changes at the
active site affecting KM [16].
Overall, the available evidence indicates that Teq and
DHeq are properties of the active site, thus explaining the
results of Tsou et al. that showed that thermally induced
loss of enzyme activity occurs at lower temperatures, and
much more rapidly, than denaturation [26,27]. This is
perhaps not surprising because it is thought that the active
site of an enzyme usually requires flexibility to carry out
catalysis, possibly leading to greater susceptibility to
temperature-induced changes in conformation and/or
dynamics. However, the data also suggest that the active
site has an additional role of controlling the effect of
temperature on the activity and the range of activity of
the enzyme over a wide range of temperatures, separate
from the effect of temperature on the kcat of the reaction.
Table 1. Effect of substrate on the EM parameters of two enzymesa
Enzyme
Subtilisin (B. subtilis)
b-glucosidase (C. saccharolyticus)
a
Substrate
Succ-AAPL-pNA
Succ-AAPNleb-pNA
pNP-fucose
pNP-xylose
DG*cat (kJ/mol)
61.4 (0.1)
61.5 (0.1)
77.0 (0.1)
84.0 (0.1)
Numbers in parentheses are fitting errors; experimental errors are 0.5% for DG*cat, DG*inact and Teq,
Norleucine.
DG*inact (kJ/mol)
98.4 (0.1)
98.7 (0.1)
101 (1)
105 (1)
and
DHeq (kJ/mol)
106 (2)
78.6 (0.6)
141 (2)
112 (1)
Teq (K)
336 (1)
323 (1)
349 (1)
338 (1)
6% for DHeq [33].
b
5
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Figure 2. The effect of temperature on initial (t0) rates for two enzymes with different DHeq values, showing the effect of DHeq on the temperature sensitivity of the Eact/Einact
equilibrium. The lines represent the initial (t0) activity of two enzymes at various temperatures based on their EM parameters derived from experimental data: Pseudomonas
dulcis b-glucosidase (broken line) (DHeq = 100 kJ/mol) and Escherichia coli malate dehydrogenase (unbroken line) (DHeq = 619 kJ/mol). On each curve, at a variety of
temperatures, the proportion of the enzyme in the Einact form is given as a percentage value. The Teq value for each enzyme is also given.
The precise details of the local changes occurring in any
specific enzyme as the equilibrium shifts from Eact to Einact
have yet to be determined. This determination might not
be simple because any structural difference between the
two forms is evidently small, and significant time constraints will be imposed by the rapid denaturation of most
enzymes at the temperatures required to yield a dominating proportion of Einact. The physical basis of the Eact/Einact
equilibration is presumably some combination of conformational, dynamic and solvent-based effects driving a
change affecting the active site. There is no reason to
expect the mechanism to be the same in all enzymes,
and it seems likely that the mechanisms will be as diverse
as the enzymes themselves.
Implications of the Equilibrium Model
One of the findings arising from the application of the EM
is that some enzymes have Teq values that are near their
expected operating temperatures [8,16,28]. In the case of
these enzymes, it is possible for a significant fraction of the
enzyme to be in the inactive state at a likely assay temperature, leading to potential underestimation of the catalytic
potential of the enzyme (Figure 2). This will depend upon
the DHeq of the enzyme, which is a measure of its ability to
function over a broad or narrow temperature range [8].
Although an evolved role for DHeq has not been shown
experimentally, it would be surprising if it were not an
adaptive property, given that different DHeq values allow
enzymes to respond differently to temperature changes,
potentially leading to desirable shifts in metabolic patterns.
Secondly, the EM might explain the results of efforts to
change the thermal properties of enzymes by mutation.
There has been a great deal of effort spent over the past 25
years using mutagenesis to increase enzyme stability, both
to understand the structural basis of protein stability and
to raise the temperature at which enzymes can usefully
6
function. Although there have been some notable successes, given that a single additional productive interaction has the potential to extend the half-life of an
enzyme by orders of magnitude [29] and that unsuccessful
attempts are unlikely to be published, the return on this
effort has been remarkably small. The EM provides a clear
rationale for this lack of success [10] (Figure 3). If the
method chosen to detect increases in DG*inact is to seek
increased activity at a higher temperature after a fixed
period of time, then any increase in stability could go
undetected because Teq is limiting activity. Furthermore,
Figure 3. A plot showing the major effects of the EM parameters on the
temperature-dependent activity of an enzyme. The value of DG*inact determines
the time-dependent loss of activity at any temperature as a result of irreversible
thermal inactivation (shown in red). When measuring initial (t0) rates, the rapid
reduction in activity at high temperatures arises from the conversion of Eact to
Einact and is governed by Teq and DHeq (blue). At any point along the time axis, the
activity of the enzyme is thus determined by all three thermodynamic
parameters.
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any actual increase in DG*inact might have little effect if Teq
then limits activity. In other words, to improve thermoactivity, both methods by which enzymes lose activity as
temperature increases – denaturation and a shift in the
Eact/Einact equilibrium – need to be addressed. In principle,
an increase in Teq could improve thermoactivity in the
absence of any rise in DG*inact.
Finally, the decrease in the initial rate (t0) plots of the
EM above a certain temperature (Box 2, Figure Ia) leads to
the counter-intuitive finding that in enzyme reactors at
temperatures above Teq, increasing temperature will
decrease both stability and reaction rates [10]. These predictions have been confirmed experimentally [M. Oudshoorn (2008) MSc thesis, University of Waikato, New
Zealand],and it is clear that the EM will have applications
in predicting optimal conditions for enzyme reactors.
Concluding remarks
Experimental results show that the active sites of
enzymes can dictate the effect of temperature on enzyme
activity, and consequently this implies that evolution of
the enzyme active site is probably constrained by its
temperature dependence. This view is entirely consistent
with, and might provide part of the rationale for, observations that the active site tends to be more flexible than
the enzyme as a whole [26,30,31]. The exact nature of the
physical changes involved are not clear, and given the
range of reactions and structures covered by the EM, they
probably are different in different enzymes, but it would be
surprising if some type of conformational change was not
involved.
Given the excellent fit to most enzymes and the good fit
to the remainder (for which Vmax data can be gathered),
the evidence that the EM accurately describes the effect
of temperature on enzymes is convincing. Nevertheless,
many enzymes do not follow ideal kinetics, for example
when the enzyme is substrate- or product-inhibited, and
the EM must be regarded as describing an ideal situation;
therefore, a degree of departure from the model might
occur, especially after significant reaction progress, as is
generally the case for all models of enzyme behaviour. It
would not be surprising if, for a particular enzyme, a more
complex equation that took these factors into account
gave a more exact fit to experimental data than did the
EM, especially where the equation has been developed to
match the experimental data from that particular
enzyme.
Finally, given that the EM is based on Vmax data, the
extent to which it applies under physiological conditions
might be assumed to depend upon the extent to which
enzymes are substrate-saturated (although ‘apparent’
parameters can be gathered under non-saturating conditions). It now seems that, in vivo, substrate saturation
might not be uncommon [32].
What began as an attempt to describe or model more
precisely the effects of temperature on enzyme activity has
led to some surprising new insights, including the discovery of a new, structurally localized mechanism for the loss
or change of enzyme activity with temperature, separate
from denaturation, and the determination of the active site
as the point of action for these effects. It has become clear
Trends in Biochemical Sciences
Vol.xxx No.x
Box 4. Outstanding questions
1) What is the molecular basis of the Eact/Einact equilibration?
2) What is the timescale of the Eact/Einact equilibration? Is it similar
for all enzymes?
3) Are there any enzymes where Vmax data do not follow the EM?
4) Is there a physiological significance to the dependence of Teq on
the nature of the substrate/cofactor?
that the EM provides a quantitative tool to investigate the
relationship between the thermal properties of enzymes
and the influence of temperature on the physiology and
evolution of the host organism. It also shows why manipulation of stability by mutation, whether naturally or by
directed mutagenesis, might not result in improved
activity at higher temperatures, and provides a strategy
by which this can be overcome. The challenge now is to
determine and perhaps exploit the molecular basis of the
EM mechanism in specific cases and to address the questions raised by the model (Box 4).
Analysis software
A Matlab version of Equation 7, to enable fitting of the raw
data (product concentration versus time) to the EM in
Excel, is available at http://hdl.handle.net/10289/3791.
Worked examples and information on validating and presenting results are provided.
Acknowledgements
This work was supported by a grant from the Royal Society of New
Zealand Marsden Fund (UOW0501). MJD gratefully acknowledges
financial support from the UK Biotechnology and Biological Sciences
Research Council, The Royal Society and the US Air Force Office of
Scientific Research. We thank John Finney and Jeremy Smith for helpful
discussions, Colin Monk for data processing and, with Max Oulton, for
assistance with the preparation of the figures. Finally, we thank all those
students, postdoctoral researchers and technicians who gathered the data
needed to test and validate the EM.
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