The kinetic equations (1) and (2) describe the reaction rates of free
enzymes. During the immobilization process, a decrease in enzyme
activity can be observed and is described by an efficiency factor
ηeff. Remaining enzyme activity after immobilization for
both FDH and ADH was determined to be 4 % of the respective free enzyme
activity. Additionally, as described in literature, a loss of activity
over time was observed for the FDH, significantly affecting the reaction
rates. This time-dependent activity loss reaches values up to 68 % and
is described in the model by the deactivation factor
fdeac. The effective reaction rates for the
dehydrogenases can be obtained after multiplying the respective kinetic
equations with the enzyme mass, while considering the aforementioned
activity losses, resulting in equation (3) for the ADH and equation (4)
for the FDH respectively.