Fed-Batch Bioproduction of Spectinomycin
43
0.4
Ke = 0.5
--' ~, ~ 0.3
.
~
0.2
0.1
0
i
~
,
.
,
!
z
r
J
t
I
f
f
~
,
i
~
,
9
,I
0
2
4
6
8
10
Glucose Concentration (g 1-1)
Fig. A.2. Position of specific growth rate for Haldane-Monod and exponential-inhibition structures.
coefficient K~. Obviously, the much higher inhibition effect experienced from the
exponential term results in this decrease. Hence, although the maximum occurs
at the same point for identical values of K,, ( = Ke) and Ki, the true significance
of these constants depend on the kinetic structure. Due to the nature of the
exponential function, the shape of the profiles are many times more sensitive
than in the Haldane-Monod kinetics. Therefore, the exponential structure
describes satisfactorily the sharp changes in slope observed in the spectinomycin
concentration, the glucose concentration, and the air flow rate profile.
Although the Monod structure is the most widely used to describe cell
growth in bioprocesses, it has two important drawbacks. First, it has a hyperbolic structure and hence the parameters of the denominator are relatively
insensitive. Second, being similar to the Michaelis-Menten kinetics, which
assumes the quasi-steady state condition of intermediates, restricts the validity
of the model to steady state operations. The Haldane-Monod kinetics which is
an extension of the Monod kinetics to circumstances where inhibition is observed, shows insensitivity in both the Monod constant Km and the inhibition
constant K~. Simulations demonstrate that the exponential structure represents
the low glucose range far better than the Monod structure. In addition, the
derivative of the exponential structure is zero at S = 0 and is the correct physical
representation of the process when substrate is absent whereas for the Monod
kinetics this value is #,,/K,,. Hence, the exponential structure is more suitable for
describing the true mechanism of spectinomycin biosynthesis accurately.
43
0.4
Ke = 0.5
--' ~, ~ 0.3
.
~
0.2
0.1
0
i
~
,
.
,
!
z
r
J
t
I
f
f
~
,
i
~
,
9
,I
0
2
4
6
8
10
Glucose Concentration (g 1-1)
Fig. A.2. Position of specific growth rate for Haldane-Monod and exponential-inhibition structures.
coefficient K~. Obviously, the much higher inhibition effect experienced from the
exponential term results in this decrease. Hence, although the maximum occurs
at the same point for identical values of K,, ( = Ke) and Ki, the true significance
of these constants depend on the kinetic structure. Due to the nature of the
exponential function, the shape of the profiles are many times more sensitive
than in the Haldane-Monod kinetics. Therefore, the exponential structure
describes satisfactorily the sharp changes in slope observed in the spectinomycin
concentration, the glucose concentration, and the air flow rate profile.
Although the Monod structure is the most widely used to describe cell
growth in bioprocesses, it has two important drawbacks. First, it has a hyperbolic structure and hence the parameters of the denominator are relatively
insensitive. Second, being similar to the Michaelis-Menten kinetics, which
assumes the quasi-steady state condition of intermediates, restricts the validity
of the model to steady state operations. The Haldane-Monod kinetics which is
an extension of the Monod kinetics to circumstances where inhibition is observed, shows insensitivity in both the Monod constant Km and the inhibition
constant K~. Simulations demonstrate that the exponential structure represents
the low glucose range far better than the Monod structure. In addition, the
derivative of the exponential structure is zero at S = 0 and is the correct physical
representation of the process when substrate is absent whereas for the Monod
kinetics this value is #,,/K,,. Hence, the exponential structure is more suitable for
describing the true mechanism of spectinomycin biosynthesis accurately.