Michaelis−Menten Case Study
Reaction scheme and dynamic
model
The case study considered in the current article uses a nonlinear
kinetic model based on a Michaelis−Menten batch reaction for the
production of a pharmaceutical agent. Domagalski et al. (2015) used this
case study to develop empirical models based on conventional DoE and
response surface methodology.6 We used the same case
study to develop and test the LO approach for V-optimal MBDoE in
previous work.21 The reaction starts with reagent SM1
reacting with catalyst D and generating intermediate SM1.D via
reversible reaction (1) in Figure 1. Next, intermediate SM1.D reacts
with reagent SM2 to make the product P and release the catalyst (i.e.,
reaction (2)). There is also a possibility of generating several
impurities: SM2 can react with P to generate impurity I1, SM1 can be
hydrolyzed to form impurity I2, D can be deactivated with water to make
I3, and P can degrade to generate I4. Table 3 provides a fundamental
dynamic model for the Michaelis−Menten batch reaction system. Equations
(3.11) to (3.14) show that the concentrations of SM1, D, SM2, and P are
measured, and these measurements have experimental errors. We assume
that the water concentration \(C_{H2O}\) and the solution volume \(V\)are constant at 0.10 M and \(1.0\ L\), respectively.
In the study by Domagalski et al., 3 rounds of simulated experiments
were performed. In each round, they conducted 16 fractional-factorial
runs + 4 center-point-runs (i.e., 20 experiments in each round and 60
overall). Table 4 shows Domagalski’s center-point settings for their
first round of experimentation. We assume that data for the 4 replicated
center-point runs are available for initial parameter estimation and
construction of \(\mathbf{Z}_{\mathbf{\text{old}}}\). Step-by-step
computation of \(\mathbf{Z}_{\mathbf{\text{old}}}\) using these runs is
described in the Supplementary Information. The duration of each
simulated batch experiment is 6.0 h with measurements taken every 45
minutes, resulting in sampling at 9 times including the initial time\(t=0\). As a result, each run involves\(\ 36\) measured values (i.e.,
9 values each for \(y_{SM1}\), \(y_{D}\), \(y_{SM2}\) and \(y_{P}\)).