Food Lipids: Chemistry, Nutrition, and Biotechnology

substrate diffuses further into the pores to reach enzyme molecules that have not
been inactivated. In systems free of diffusional limitations, enzyme inactivation follows
a first-order decay:
N 0
ln = �t
N
where N 0 is the initial enzyme activity, N is the activity at time t, and � is the decay
constant. Using �, the half-life of the immobilized lipase can be determined as
follows:
0.693
half-life =
�
The half-lives of lipases in interesterification systems have been reported to range
from 7 minutes to 7 months, with the large variability attributed to the source of
lipases and different reaction conditions (50). As previously stated, the half-life of
the immobilized enzyme can be used to determine the productivity of the system. In
order to avoid losses in productivity as the activity of the immobilized lipase decreases,
the temperature can be raised to increase the reaction rate or, in fixed bed
reactor systems, the flow rate can be reduced (80). While these measures can improve
the conversion rate, they can also increase the rate of enzyme inactivation in the
case of temperature increases, or decrease the throughput in the case of reduced flow
rate.
C. Immobilized Enzyme Kinetics
The previous discussion on the kinetics of lipase action was developed for soluble
lipases acting on insoluble substrate, but assuming that diffusional and mass transfer
effects are not rate-limiting, the same theories can be applied to immobilized lipases.
When using immobilized lipases, the level of substrate in comparison with the level
of enzyme must be considered. In general, there is a low average concentration of
substrate in direct contact with the immobilized lipase due to high conversion rates,
producing first-order, mixed first and zero-order, or zero-order kinetics as opposed
to zero-order Michaelis–Menten kinetics (80). The rate of the reaction, v, is proportional
to the substrate concentration at the interface where
V [S]
max
v = K � [S]
m
The kinetics of immobilized lipases are also affected by the type of reactor used,
since reactors differ in the amount of immobilized lipase used and in the method of
substrate delivery, product removal, and degree of mixing.
V. ENZYMATIC INTERESTERIFICATION REACTORS
Reactors designed for immobilized enzyme reactions differ from one another based
on several criteria. Reactors can be batch or flow-through systems and can differ in
the degree of mixing involved during the reaction. For all reactor systems, the productivity
of the system is defined as the volumetric activity � the operational stability
of the immobilized enzyme, with units of kilograms of product per liter of reactor
Copyright 2002 by Marcel Dekker, Inc. All Rights Reserved.