Enzyme Technology
Effect of temperature and pressure
Rates of all reactions, including those
catalysed by enzymes, rise with increase in temperature in accordance with the
Arrhenius equation.
(1.21)
where
k is the kinetic rate constant for the reaction, A is the Arrhenius constant,
also known as the frequency factor, DG* is the standard free
energy of activation (kJ M−1) which depends on entropic and enthalpic
factors, R is the gas law constant and T is the absolute temperature. Typical
standard free energies of activation (15 - 70 kJ M−1) give rise to
increases in rate by factors between 1.2 and 2.5 for every 10°C rise
in temperature. This factor for the increase in the rate of reaction for every
10°C rise in temperature is commonly denoted by the term
Q10 (i.e., in this case, Q10 is within the
range 1.2 - 2.5). All the rate constants contributing to the catalytic mechanism
will vary independently, causing changes in both Km and
Vmax. It follows that, in an exothermic reaction, the reverse reaction
(having a higher activation energy) increases more rapidly with temperature than
the forward reaction. This, not only alters the equilibrium constant (see
equation 1.12), but also reduces the optimum temperature for maximum conversion
as the reaction progresses. The reverse holds for endothermic reactions such as
that of glucose isomerase (see reaction [1.5]) where the ratio of fructose to
glucose, at equilibrium, increases from 1.00 at 55°C to 1.17 at
80°C.
In general, it would be preferable to use enzymes at high
temperatures in order to make use of this increased rate of reaction plus the
protection it affords against microbial contamination. Enzymes, however, are
proteins and undergo essentially irreversible denaturation (i.e..
conformational alteration entailing a loss of biological activity) at
temperatures above those to which they are ordinarily exposed in their natural
environment. These denaturing reactions have standard free energies of
activation of about 200 - 300 kJ ˣ mol−1 (Q10 in the range 6
- 36) which means that, above a critical temperature, there is a rapid rate of
loss of activity (Figure 1.5). The actual loss of activity is the product of
this rate and the duration of incubation (Figure 1.6). It may be due to covalent
changes such as the deamination of asparagine residues or non-covalent changes
such as the rearrangement of the protein chain. Inactivation by heat
denaturation has a profound effect on the enzymes productivity (Figure
1.7).
Figure
1.5. A schematic diagram showing the effect of the temperature on the
activity of an enzyme catalysed reaction. ——
short incubation period;
----- long incubation period. Note that the temperature at which there appears
to be maximum activity varies with the incubation time.
Figure 1.6. A
schematic diagram showing the effect of the temperature on the stability of an
enzyme catalysed reaction. The curves show the percentage activity remaining as
the incubation period increases. From the top they represent equal increases in
the incubation temperature (50°C, 55°C, 60°C, 65°C and 70°C).
Figure
1.7. A schematic diagram showing the effect of the temperature on the
productivity of an enzyme catalysed reaction. ——
55°C; ——
60°C; —— 65°C. The optimum productivity
is seen to vary with the process time, which may be determined by other
additional factors (e.g., overhead costs). It is often difficult to get precise
control of the temperature of an enzyme catalysed process and, under these
circumstances, it may be seen that it is prudent to err on the low temperature
side.
The thermal denaturation of an enzyme may be modelled by
the following serial deactivation scheme:
[1.11]
where kd1 and
kd2 are the first-order deactivation rate coefficients, E is the
native enzyme which may, or may not, be an equilibrium mixture of a number of
species, distinct in structure or activity, and E1 and E2
are enzyme molecules of average specific activity relative to E of A1
and A2. A1 may be greater or less than unity (i.e.
E1 may have higher or lower activity than E) whereas A2 is
normally very small or zero. This model allows for the rare cases involving free
enzyme (e.g., tyrosinase) and the somewhat commoner cases involving immobilised
enzyme (see Chapter 3) where there is a small initial activation or period of
grace involving negligible discernible loss of activity during short incubation
periods but prior to later deactivation. Assuming, at the beginning of the
reaction:
(1.22)
and:
(1.23)
At time t,
(1.24)
It follows from the reaction
scheme [1.11],
(1.25)
Integrating equation 1.25 using the boundary
condition in equation 1.22 gives:
(1.26)
From the reaction
scheme [1.11],
(1.27)
Substituting for [E] from equation 1.26,
(1.28)
Integrating
equation 1.27 using the boundary condition in equation 1.23 gives:
(1.29)
If the term 'fractional activity' (Af) is
introduced where,
(1.30)
then, substituting for
[E2] from equation 1.24, gives:
(1.31)
therefore:
(1.32)
When both A1 and A2 are zero, the
simple first order deactivation rate expression results
(1.33)
The half-life
(t1/2) of an enzyme is the time it takes for the activity to reduce to
a half of the original activity (i,e. Af = 0.5). If the enzyme
inactivation obeys equation 1.33, the half-life may be simply derived,
(1.34)
therefore:
(1.35)
In this simple case, the half-life of the
enzyme is shown to be inversely proportional to the rate of denaturation.
Many
enzyme preparations, both free and immobilised, appear to follow this
series-type deactivation scheme. However because reliable and reproducible data
is difficult to obtain, inactivation data should, in general, be assumed to be
rather error-prone. It is not surprising that such data can be made to fit a
model involving four determined parameters (A1, A2,
kd1 and kd2). Despite this possible reservation, equations
1.32 and 1.33 remain quite useful and the theory possesses the definite
advantage of simplicity. In some cases the series-type deactivation may be due
to structural microheterogeneity, where the enzyme preparation consists of a
heterogeneous mixture of a large number of closely related structural forms.
These may have been formed during the past history of the enzyme during
preparation and storage due to a number of minor reactions, such as deamidation
of one or two asparagine or glutamine residues, limited proteolysis or
disulphide interchange. Alternatively it may be due to quaternary structure
equilibria or the presence of distinct genetic variants. In any case, the larger
the variability the more apparent will be the series-type inactivation kinetics.
The practical effect of this is that usually kd1 is apparently much
larger than kd2 and A1 is less than unity.
In order to minimise loss of activity on storage, even moderate temperatures should be
avoided. Most enzymes are stable for months if refrigerated (0 - 4°C).
Cooling below 0°C, in the presence of additives (e.g., glycerol) which
prevent freezing, can generally increase this storage stability even further.
Freezing enzyme solutions is best avoided as it often causes denaturation due to
the stress and pH variation caused by ice-crystal formation. The first order
deactivation constants are often significantly lower in the case of
enzyme-substrate, enzyme-inhibitor and enzyme-product complexes which helps to
explain the substantial stabilising effects of suitable ligands, especially at
concentrations where little free enzyme exists (e.g. [S] >> Km).
Other factors, such as the presence of thiol anti-oxidants, may improve the
thermal stability in particular cases.
It has been found that the heat
denaturation of enzymes is primarily due to the proteins' interactions with the
aqueous environment. They are generally more stable in concentrated, rather than
dilute, solutions. In a dry or predominantly dehydrated state, they remain
active for considerable periods even at temperatures above 100°C. This
property has great technological significance and is currently being exploited
by the use of organic solvents (see Chapter 7).
Pressure changes will also affect
enzyme catalysed reactions. Clearly any reaction involving dissolved gases (e.g., oxygenases and decarboxylases) will be particularly affected by the increased
gas solubility at high pressures. The equilibrium position of the reaction will
also be shifted due to any difference in molar volumes between the reactants and
products. However an additional, if rather small, influence is due to the volume
changes which occur during enzymic binding and catalysis. Some enzyme-reactant
mixtures may undergo reductions in volume amounting to up to 50 ml
mole−1 during reaction due to conformational restrictions and changes
in their hydration. This, in turn, may lead to a doubling of the kcat,
and/or a halving in the Km for a 1000 fold increase in pressure. The
relative effects on kcat and Km depend upon the relative
volume changes during binding and the formation of the reaction transition
states.
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This page was established in 2004 and last updated by Martin
Chaplin on
6 August, 2014
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