Modeling of Growth Kinetics
303
result of the differentiation processes, a reasonable hypothesis for many secondary metabolites. The
model describes several general observations concerning growth of
A. awamori
, and it is a nice
example of how morphological structure can be used to describe a very complex system. A
disadvantage of the model is the large number of parameters, but for simulation of submerged
growth one may neglect spore formation and consider only actively growing hyphae, i.e., the
morphological forms ZA
and ZH. Thereby the original model is substantially simplified, as
illustrated in Example 7.10. *
Example 7,10 A simple morphologically structured model for growth of filamentous microorganisms
Based on the growth mechanisms described above Nielsen (1993) derived a simple morphologically
structured model including the three morphological forms shown in Fig. 7.20:
Apical cells (ZA)
Subapical cells (Zs)
Hyphal cells (ZH)
The model is a progeny of the Megee
et al.
model. The verbal formulation of the model is:
Active growth, i.e., uptake of substrates and formation of biomass, occurs only in apical and
subapical cells. When the tip extends, an apical cell is converted to a subapical cell, whereas a
new apical cell is produced from subapical cell material when a branch point is formed in the
subapical compartment. When the subapical cells become more and more vacuolated, they change
into inactive hyphal cells.
The mathematical formulation is given in Eqs. (1) and (2). Three metamorphosis reactions described in
matrix form in Eq. (1) are considered. They represent branching, tip growth, and differentiation,
respectively. The kinetics of all three metamorphosis reactions is taken to be first order in the
morphological form which disappears. Furthermore, formation of inactive hyphae is assumed to be
inhibited by high substrate concentrations. The Monod model describes growth of both the apical and
subapical cells, where
s
is the extracellular glucose concentration.
' 1
~1
-1
1
, 0
” 1
o Y O
o
*
A z h j
'<T|
0
(u \
v“ 3
y
k 2Z A
Jc^Zs /(sK 2
+ V);
- a >
(1
0
°1
f z A
f ° l
- a s
s
+
0
1
0
z s
=
0
o
J
,0
0
0;
\Z H j
,0 ;
w
'k As/(s + K s)^
Ms
=
kss/(s + K s)
J
K
0
J
0 )
(
2
)
Inserting (1) and (2) in (7.67), (7.68) one obtains the specific growth rate of the total biomass and the mass
balances for the three morphological forms:
s + K ,
p.
(kAZ A + ksZ s )
(3)
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