ForT 4 Tden;K 4 1, andkobs&ki, and the latter probably has a weak
temperature dependence as compared to ku.AtT 5 Tden;K 5 1, and
kobs&kiK. Now the temperature dependence will be very strong:Kstrongly
depends onT(see, e.g., Figure 7.4a), and although this is far less so forki,
the dependence of the reaction rate on temperature is as the product of both
variables.
It will now depend on the magnitude ofkiatTden(whereK¼1) what
is observed, taking into account that the values ofkobswould range between
about 3? 10 ^4 and 1 s^1 in practice (heating times between 1 s and 1 h). Ifki
is very small, denaturation is negligible. If, for instance,ki¼ 0 :1s^1 at
Tden;kobs¼ 0 :05 s^1 ; in such a case a strong temperature dependence will be
observed at lowT, gradually changing to a weak dependence at highT.
Several enzymes show such behavior, and an example is given by plasmin
(Figures 4.6 and 7.9). Ifki is large, say 10^3 s^1 , only the steep relation
between reaction rate and temperature is experimentally accessible, and
kobs¼kiK.
The last case is the most common one for enzyme inactivation and it is
nearly always observed for the killing of microorganisms. The latter is to be
explained by the fact that the killing of a microbe will depend on irreversible
inactivation of the most unstable of its essential enzymes, and that would be
one following the inactivation pathway discussed here, since the other
situations imply a smaller ki and would therefore imply greater heat
stability.
Note. On the other hand, microbes of one species, or even of one
strain, show some physiological variation in heat stability, which
may possibly affect curves like those in Figure 7.9.Complications. In several cases, other relations are observed, and
only for some of these have fitting explanations been found. From such
studies, supplemented with some reasoning, the following complications
may be derived. It will often be difficult to distinguish between them. We
will not discuss the various types of kinetics observed or derived from
inactivation models.
- Intermediate stepsin reaching the unfolded state. One example is
dissociation of quaternary structure. This is not uncommon, since several
enzymes exhibit such structures, which often are essential for enzyme
activity. Another possibility is unfolding in steps, as mentioned in Section
7.2.1. Such complications can in principle cause so-called grace-period
behavior (Figure 7.11a) as well as the opposite, i.e., decelerating
inactivation. The latter may be a gradual decrease in rate, or there may
be two fairly distinct first order stages, as shown in Figure 711.b.