2009_Book_FoodChemistry

2.5 Kinetics of Enzyme-Catalyzed Reactions 133
and
lnt =+ E a
+ const. (2.100)
RT
When plotting lnt against 1/T, a family of parallel
lines results for each of different activation
energies E a with each line from a family corresponding
to a constant effect c t /c 0 (cf. equation
2.99) (Fig. 2.34).
For very narrow temperature ranges, sometimes
a diagram representing log t against temperature δ
(in ◦ C) is favourable. It corresponds to:
log t E a
= −
t B 2.3R · T B · T (ϑ − ϑ B)= 1 z (ϑ − ϑ B)
(2.101)
with t B as reference time and T B or δ B as
reference temperature in K respectively ◦ C.
For logt/t B the following is valid:
z = 2.3R · T B · T
(2.102)
E a
This z-value, used in practice, states the temperature
increase in ◦ C required to achieve a certain
effect in only one tenth of the time usually
needed at the reference temperature. However,
due to the temperature dependence of the z-
value (equation 2.101), linearity can be expected
for a very narrow temperature range only. A plot
according to equation 2.100 is therefore more
favourable.
In the literature, the effect of thermal processes is
often described by the Q 10 value. It refers to the
ratio between the rates of a reaction at temperatures
δ + 10( ◦ C) and δ( ◦ C):
Q 10 = k ϑ+10
= t ϑ
(2.103)
k ϑ t ϑ+10
The combination of equations 2.101 and 2.103
shows the relationship between the Q 10 value and
z-value:
logQ 10
10
= E a
2.3RT 2 = 1 z
(2.104)
2.5.4.3 Temperature Optimum
Fig. 2.34. Lines of equal microbiological and chemical
effects for heat-treated milk (lines B10, B1, and BO.1
correspond to a reduction in thermophilic spores by
90, 9, and 1 power of ten compared to the initial
load; lines C10, C1, and CO.1 correspond to a thiamine
degradation of 30%, 3%, and 0.3%; according
to Kessler, 1988)
Contrary to common chemical reactions,
enzyme-catalyzed reactions as well as growth of
microorganisms show a so-called temperature
optimum, which is a temperature-dependent
maximum resulting from the overlapping of
two counter effects with significantly different
activation energies (cf. 2.5.4.2):
• increase in reaction or growth rate
• increase in inactivation or killing rate
For starch hydrolysis by microbial α-amylase, the
following activation energies, which lie between
the limits stated in section 2.5.4.2, were derived
from e. g. the Arrhenius diagram (Fig. 2.35):
• E a (hydrolysis) = 20 kJ · mol −1
• E a (inactivation) = 295 kJ · mol −1
As a consequence of the difference in activation
energies, the rate of enzyme inactivation is substantially
faster with increasing temperature than
the rate of enzyme catalysis. Based on activation
energies for the above example, the following
relative rates are obtained (Table 2.14). Increasing
δ from 0 to 60 ◦ C increases the hydrolysis rate
by a factor of 5, while the rate of inactivation is
accelerated by more than 10 powers of ten.