Food Chemistry

2.5 Kinetics of Enzyme-Catalyzed Reactions 133

and

lnt=+

Ea

RT

+const. (2.100)

When plotting lnt against 1/T, a family of par-
allel lines results for each of different activation
energies Eawith each line from a family cor-
responding to a constant effect ct/c 0 (cf. equa-
tion 2.99) (Fig. 2.34).
For very narrow temperature ranges, sometimes
a diagram representing log t against temperatureδ
(in◦C) is favourable. It corresponds to:

log

t

tB

=−

Ea

2 .3R·TB·T

(θ−θB)=

1

z

(θ−θB)

(2.101)

with tB as reference time and TB orδB as
reference temperature in K respectively ◦C.
For logt/tBthe following is valid:

z=

2 .3R·TB·T

Ea

(2.102)

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 thi-
amine degradation of 30%, 3%, and 0.3%; according
toKessler, 1988)

This z-value, used in practice, states the tempera-

ture increase in◦C required to achieve a cer-

tain effect in only one tenth of the time usu-

ally needed at the reference temperature. How-

ever, 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 tempera-

turesδ+ 10 (◦C)andδ(◦C):

Q 10 =

kθ+ 10

kθ

=

tθ

tθ+ 10

(2.103)

The combination of equations 2.101 and 2.103

shows the relationship between the Q 10 value and

z-value:

logQ 10

10

=

Ea

2 .3RT^2

=

1

z

(2.104)

2.5.4.3 TemperatureOptimum

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 microbialα-amylase, the
  following activation energies, which lie between
  the limits stated in section 2.5.4.2, were derived
  from e. g. theArrheniusdiagram (Fig. 2.35):
  •Ea(hydrolysis)=20 kJ·mol−^1
  •Ea(inactivation)=295 kJ·mol−^1
  As a consequence of the difference in activation
  energies, the rate of enzyme inactivation is sub-
  stantially faster with increasing temperature than
  the rate of enzyme catalysis. Based on activa-
  tion energies for the above example, the following
  relative rates are obtained (Table 2.14). Increas-
  ingδfrom 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.