## 3 Results
### Kinetic Studies Using MME and IMME Based on Simulated Values  
When reactions are carried out in the presence of a second inhibitor, another set of integrated equations assumes the simultaneous presence of two mutually exclusive inhibitors (Figure 1b), where one of which is a reaction product. This process is presented in Table 2 [8]. In the presence of two inhibitors, a linear MI model (Equation (9), Table 2) can be simplified into other nested models with fewer parameters (Equations (1), (6)-(8), assuming that constants \(\mathrm{K_{ic1}}\), \(\mathrm{K_{ic2}}\), \(\mathrm{K_{iu1}}\), \(\mathrm{K_{iu2}}\) tend to infinity (WI, Equation (1)) or only some of them do (CI or UCI, (Equations (6) and (8)), or when \(\mathrm{K_{ic1}}=\mathrm{K_{iu1}}\) and \(\mathrm{K_{ic2}}=\mathrm{K_{iu2}}\) (NCI, Equation (7)). \begin{table}
\begin{tabular}{c c} \hline \hline
**Kinetic Model \({}^{\star}\)** & \\ \hline CI & \(t=-\frac{1}{\mathrm{Var}_{\mathrm{max}}}\left\{K_{\mathrm{in}}\left(\frac{[S_{ 0}]}{K_{\mathrm{ic1}}}+\frac{[S_{1}]}{K_{\mathrm{ic1}}}+\frac{[S_{1}]}{K_{ \mathrm{ic2}}}+1\right)ln\frac{[S_{1}]}{[S_{0}]}+\left(1-\frac{K_{\mathrm{in}} }{K_{\mathrm{ic1}}}\right)([S_{1}]-[S_{0}])\right\}\) & (6) \\ NCI & (7) \\ UCI & (8) \\ MI & (9) \\ \hline \hline \end{tabular}  
* CI—competitive inhibition; NCI—noncompetitive inhibition; UCI—uncompetitive inhibition; MI—mixed inhibition.  
\end{table} 
Table 2: Integrated Michaelis–Menten equations obtained from the model explained in Figure 1, considering the simultaneous presence of two mutually exclusive inhibitors when one of which is a reaction product [8]. Thus, initial velocity studies in the presence of reaction product inhibition have two implicit drawbacks: (1) the initial velocities of these two equations (without product inhibition and with product inhibition) are the same; and (2) it is assumed that the initial velocities are data points belonging to the Michaelis-Menten equation (V\({}_{0}\) = V\({}_{\text{max}}\) [S]/(K\({}_{\text{m}}\) + [S]). These methodological simplifications were overlooked about 100 years ago when it was very difficult to overcome these problems due to the lack of computers. Even after computer use became common, the determination of initial velocities when the product of the reaction is an inhibitor remains very popular. In kinetic studies, equations must be adjusted to the data points prior to the discrimination of the best model. Unfortunately, in almost all published studies, data points were adjusted to the equations that were previously assumed to be correct. Thus, miscalculation begins with the initial velocity determinations when the reaction product inhibition is not considered [15, 16]. The error can even be accentuated when, in many cases, the data points are adjusted to a particular inhibition model without considering other types of inhibition, which may provide better adjustments (e.g., non-competitive versus mixed inhibition). Inaccuracies are also amplified when the kinetics are studied using archic curve linearization, such as with the popular Lineweaver-Burk plot, which is still used today [17], or other similar processes. The advantages of integrated equations have been presented by many authors and summarized in previous publications [8, 9, 10, 12, 18, 19, 20]. To emphasize the importance of this subject, misinterpretations can be increased when another different inhibitor is added to the reaction medium, which is a mandatory condition in kinetic inhibition studies [8, 9].