Modeling of Growth Kinetics
305
where a2 is physiological constant determined by the mass of apical compartment per tip. Finally the tip
extension rate
can be derived from the hyphal growth unit length and the specific growth rate:
Чир
=
& h&
(?)
With the morphologically structured model the fraction of the morphological forms can be calculated and
using Eqs. (5)-(7) it is then possible to calculate the development of directly measurable morphological
variables.
The model was compared with experimental data for
G. candidum, Streptomyces hygroscopious,
and
Penicillium chrysogenum,
and in Fig. 7.21 and 7.22 the results of the comparison with data for
G. candidum
are shown.
In Fig. 7.21, measurements of the hyphal diameter, the hyphal growth unit volume, and the hyphal growth
unit length in a steady-state chemostat are shown as functions of the dilution rate
D,
The hyphal diameter
increases with
D,
and since the hyphal growth unit volume is approximately constant, /hgu decreases with the
dilution rate. Thus, when the glucose concentration decreases, the hyphal elements become less branched
and form long hyphae. In Fig. 7.22, measurements of the total hyphal length, the number of tips, and the
hyphal growth unit length during outgrowth of a single spore on a solid medium are shown, together with
model simulations. The total hyphal length is observed to increase exponentially, whereas there is a lag
phase before the first branch point is formed, i.e., the number of tips increases from one to two. Due to the
sudden formation of new tips the hyphal growth unit length oscillates until the number of tips becomes
large and an approximately constant value for /hgu is obtained. The modeling concept illustrated in this
example has been applied for simulation of many other systems, e.g. for enzyme production by
Aspergillus
oryzae
(Agger
et al,
1998). Recent reviews on modeling of filamentous fungi are given by Nielsen (1996)
and Krabben and Nielsen (1998).
Dilution rat# {h'1}
Figure 7.21 Morphology of
G. candidum
as a function of the specific growth rate in a submerged
culture. Hyphal growth unit length, hyphal growth unit volume, and the hyphal diameter are shown as
functions of the dilution rate in a chemostat. Lines are model simulations. The experimental data are
taken from Robinson and Smith (1979) and model simulations are from Nielsen (1993).
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