44
J. Gomes and A.S. Menawat
The exponential form is excellent for parameter estimation. When converted
into its logarithmic equivalent the resulting algebraic equation contains all the
parameters independent of each other and in their native forms. This characteristic increases the sensitivity and accuracy in the estimation of its parameters.
The exponential kinetics,
#(S) = #m exp (- ~--1~) exp (- ~)
(A.4)
where Ke is the exponential model constant equivalent to the Monod constant
K,, and K, is the inhibition constant, reduces to the form
S
Ke
In # -
+ In #m
(A.5)
Ki
S
suitable for parameter estimation. The Haldane-Monod structure under similar
manipulation gives
S#
#Kin
# = - K~. + #" -- T
(a.6)
The states of Eq. (A.6) cannot be decoupled. Consequently, parameter estimation from the Haldane-Monod kinetics suffers from problems associated with
interaction and insensitivity. In the case of the exponential structure, a simple
regression on the substrate data gives the estimates of the parameters. Whereas,
for the Haldane-Monod kinetics, the coupled parameters make it difficult to
estimate their value. The procedure is not straight forward because by coupling,
such as, I~/S and #S, the states lose their individual properties and the associated
errors amplify by propagation. This results in inaccuracies in the estimates of all
three parameters. Therefore, from the discussions above we conclude that the
exponential structure contains more characteristics for describing spectinomycin bioproduction. Furthermore, data analysis is easier in the exponential
form. Above all, the exponential kinetics reduces to the Monod-type structure
under special conditions.
Mechanistic Model
We have established in Section 5 that there are two alternate routes for the
biosynthesis of spectinomycin. In these alternate routes, two different metabolites, Pt and P2, contribute to the final concentration of spectinomycin. Since
the final concentration of spectinomycin depends on the concentrations of
Px and P2, we assume that the observed concentration of spectinomycin is the
sum of the concentrations of P1 and P2. The other variables describing the
fermentation are the substrate (glucose) concentration S, cell mass concentration
C and the dissolved oxygen (from air) concentration A. We assume that both
products P1 and Pz degrade at a constant rate Kd. Then the equations for the
J. Gomes and A.S. Menawat
The exponential form is excellent for parameter estimation. When converted
into its logarithmic equivalent the resulting algebraic equation contains all the
parameters independent of each other and in their native forms. This characteristic increases the sensitivity and accuracy in the estimation of its parameters.
The exponential kinetics,
#(S) = #m exp (- ~--1~) exp (- ~)
(A.4)
where Ke is the exponential model constant equivalent to the Monod constant
K,, and K, is the inhibition constant, reduces to the form
S
Ke
In # -
+ In #m
(A.5)
Ki
S
suitable for parameter estimation. The Haldane-Monod structure under similar
manipulation gives
S#
#Kin
# = - K~. + #" -- T
(a.6)
The states of Eq. (A.6) cannot be decoupled. Consequently, parameter estimation from the Haldane-Monod kinetics suffers from problems associated with
interaction and insensitivity. In the case of the exponential structure, a simple
regression on the substrate data gives the estimates of the parameters. Whereas,
for the Haldane-Monod kinetics, the coupled parameters make it difficult to
estimate their value. The procedure is not straight forward because by coupling,
such as, I~/S and #S, the states lose their individual properties and the associated
errors amplify by propagation. This results in inaccuracies in the estimates of all
three parameters. Therefore, from the discussions above we conclude that the
exponential structure contains more characteristics for describing spectinomycin bioproduction. Furthermore, data analysis is easier in the exponential
form. Above all, the exponential kinetics reduces to the Monod-type structure
under special conditions.
Mechanistic Model
We have established in Section 5 that there are two alternate routes for the
biosynthesis of spectinomycin. In these alternate routes, two different metabolites, Pt and P2, contribute to the final concentration of spectinomycin. Since
the final concentration of spectinomycin depends on the concentrations of
Px and P2, we assume that the observed concentration of spectinomycin is the
sum of the concentrations of P1 and P2. The other variables describing the
fermentation are the substrate (glucose) concentration S, cell mass concentration
C and the dissolved oxygen (from air) concentration A. We assume that both
products P1 and Pz degrade at a constant rate Kd. Then the equations for the