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 \(y_{P}\)).