Bio Effect of Temperature on Enzymes

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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 10oC rise in temperature. This factor for the increase in the rate of reaction for every 10oC 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 55oC to 1.17 at 80oC.

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 mole-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).

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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.

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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 (50oC, 55oC, 60oC, 65oC and 70oC).

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Figure 1.7. A schematic diagram showing the effect of the temperature on the productivity of an enzyme catalysed reaction. ---- 55oC; ---- 60oC; ---- 65oC. 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.

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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