of fermentation linked together to achieve a degree of
overlap during the batch. The expressions used for the
growth rate employed different values for μmax derived
in different phases. Although the model allowed more
than one rate expression to be valid at the same time, a
situation in which all the expressions were valid was not
likely to arise. The model was quite complex and it
could not accurately simulate the experimental results
for different batch conditions.
5.6. Morphologically structured modeling by Bizukojc
and Ledakowicz (2006)
Structured modeling of microbial processes implies
that cells are not treated as a “black box” in which neither
intracellular metabolic reactions nor microbial morphology
are taken into account. The morphologically
structured model for A. niger proposed by Bizukojc and
Ledakowicz (2006) was based on the mathematical
modeling framework formulated by Nielsen and Villadsen
(1994). The model took into consideration six
extracellular components that were detected in the
fermentation medium. Hyphae were divided into four
zones of different physiological and functional states. The
model consisted of ten ordinary differential equations that
balanced biomass in the different hyphal zones and
included the effects of the most important nutrients and
products (i.e. carbon sources, nitrogen source, citric acid).
The model established a direct linear correlation between
the physiological zone B (a less metabolically active and
more vacuolated area) and citric acid excretion, confirming
that this particular hyphal zone was responsible for
acid excretion. A good agreement was found between the