26
J. Gomes and A.S. Menawat
synthesis through a series of enzymatic reactions. Spectinomycin synthesis
continues until it saturates at first level. The deactivation or inhibition of the first
route of biosynthesis is followed by the activation of spectinomycin synthesis
through an alternate route. This happens when the environmental conditions
can no longer support the synthesis of spectinomycin by the first pathway. As
before, the synthesis of spectinomycin continues until it saturates at some new
level. Hence, spectinomycin biosynthesis follows an activation-reaction-inhibition sequence of events. Clearly two separate routes are involved in which two
different key intermediates, 1,3 myo-inosadiamine and actinospectose, participate. Therefore, the activation-reaction-inhibition sequence holds for each of the
two intermediates participating in the biosynthesis of spectinomycin.
A mathematical description of the process should also incorporate parameter sensitivity, both geometric and numerical, for implementation in process
control. Geometric sensitivity enables a close tracking of the actual experimental data profile, whereas numerical sensitivity reduces computation time
and allows accurate parameter evaluation. This is vital for spectinomycin
biosynthesis because the lag phase is considerable. The subsequent increase in
concentration is steep and there are two saturation levels. To describe these
rapid changes in the profile an exponential variation of the Monod kinetics is
developed here.
Assuming that the overall rate is inhibited according to first order kinetics,
and applying an exponential variation of the Monod equation (see Appendix),
the following exponential inhibition kinetics is obtained.
where #m is the maximum specific growth rate, Ke is the exponential equivalent
of the Monod constant Kin, Ki is the inhibition constant and S is the substrate
concentration. The first exponential component exp(- Ke/S) is the reaction
term and the second exponential component exp( - S/KO is the inhibition term.
This is the exponential structure used to describe the biosynthesis of spectinomycin. The model equations (Eq. A.7) are presented in the appendix.
6.1 Model Simulation
The parameter values of the model Eq. A.7 obtained along with the sum of the
squares of the error per data point are also presented in Table 2. These errors are
the combined sum of errors for spectinomycin and residual glucose concentrations per data point. Tio, which denotes the starting times for glucose feeding is
known from the recorded data. The parameters presented in Table 2 were
computed by nonlinear regression and excluded the last two data points in each
of the data sets. The last two data points were excluded because the regulatory
mechanism governing this phenomenon is not accounted in the model. Such
J. Gomes and A.S. Menawat
synthesis through a series of enzymatic reactions. Spectinomycin synthesis
continues until it saturates at first level. The deactivation or inhibition of the first
route of biosynthesis is followed by the activation of spectinomycin synthesis
through an alternate route. This happens when the environmental conditions
can no longer support the synthesis of spectinomycin by the first pathway. As
before, the synthesis of spectinomycin continues until it saturates at some new
level. Hence, spectinomycin biosynthesis follows an activation-reaction-inhibition sequence of events. Clearly two separate routes are involved in which two
different key intermediates, 1,3 myo-inosadiamine and actinospectose, participate. Therefore, the activation-reaction-inhibition sequence holds for each of the
two intermediates participating in the biosynthesis of spectinomycin.
A mathematical description of the process should also incorporate parameter sensitivity, both geometric and numerical, for implementation in process
control. Geometric sensitivity enables a close tracking of the actual experimental data profile, whereas numerical sensitivity reduces computation time
and allows accurate parameter evaluation. This is vital for spectinomycin
biosynthesis because the lag phase is considerable. The subsequent increase in
concentration is steep and there are two saturation levels. To describe these
rapid changes in the profile an exponential variation of the Monod kinetics is
developed here.
Assuming that the overall rate is inhibited according to first order kinetics,
and applying an exponential variation of the Monod equation (see Appendix),
the following exponential inhibition kinetics is obtained.
where #m is the maximum specific growth rate, Ke is the exponential equivalent
of the Monod constant Kin, Ki is the inhibition constant and S is the substrate
concentration. The first exponential component exp(- Ke/S) is the reaction
term and the second exponential component exp( - S/KO is the inhibition term.
This is the exponential structure used to describe the biosynthesis of spectinomycin. The model equations (Eq. A.7) are presented in the appendix.
6.1 Model Simulation
The parameter values of the model Eq. A.7 obtained along with the sum of the
squares of the error per data point are also presented in Table 2. These errors are
the combined sum of errors for spectinomycin and residual glucose concentrations per data point. Tio, which denotes the starting times for glucose feeding is
known from the recorded data. The parameters presented in Table 2 were
computed by nonlinear regression and excluded the last two data points in each
of the data sets. The last two data points were excluded because the regulatory
mechanism governing this phenomenon is not accounted in the model. Such