## 2 Materials and Methods  
### Simulated Data for the Graphical Representation of Product Versus Time  
Simulated data representing product versus time curves with integrated equations considering the absence of product inhibition (Equation (1), Table 1 and Figure 1a) and also competitive inhibition by the reaction product (Equation (2), Table 1 and Figure 1b) were used to obtain four graphical representations of different \(\text{K}_{\text{m}}/\text{K}_{\text{i}}\) (Figure 2). The following arbitrary parameters were used in the simulation: (a) \(\text{V}_{\text{max}}=18~{}\upmu\text{M}~{}\text{min}^{-1}\); \(\text{K}_{\text{m}}=500~{}\upmu\text{M}\); \(\text{S}_{0}=100~{}\upmu\text{M}\); \(\text{K}_{\text{ic}}=0.5~{}\upmu\text{M}\); (b) \(\text{V}_{\text{max}}=18.0~{}\upmu\text{M}~{}\text{min}^{-1}\); \(\text{K}_{\text{m}}=100~{}\upmu\text{M}\); \(\text{S}_{0}=100~{}\upmu\text{M}\); \(\text{K}_{\text{ic}}=2~{}\upmu\text{M}\). \(\text{S}_{0}=100~{}\upmu\text{M}\); \(\text{K}_{\text{ic}}=2~{}\upmu\text{M}\). (d) \(\text{V}_{\text{max}}=18.0~{}\upmu\text{M}~{}\text{min}^{-1}\); \(\text{K}_{\text{m}}=2~{}\upmu\text{M}\); \(\text{S}_{0}=100~{}\upmu\text{M}\); \(\text{K}_{\text{ic}}=5~{}\upmu\text{M}\).  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Kinetic Model 1** & **Equation** \\ \hline WI & \(t=-\frac{1}{\
u_{max}}\left\{K_{\text{m}}\left[\frac{\left[S_{0}\right]}{ \kappa_{\text{c}}}+\left[\frac{1}{\kappa_{\text{c}}}+1\right]ln\left[\frac{S_{0} }{\kappa_{\text{c}}}\right]+\left(1-\frac{\kappa_{\text{m}}}{\kappa_{\text{c} }}\right)\left(\left[S_{t}\right]-\left[S_{0}\right]\right)\right\}\) & (1) \\ CI & \(t=-\frac{1}{\
u_{max}}\left\{K_{\text{m}}\left(\frac{\left[S_{0}\right]}{ \kappa_{\text{c}}}+\frac{\left[1\right]}{\kappa_{\text{c}}}+1\right)ln\left[ \frac{S_{0}}{\kappa_{\text{c}}}\right]+\left(1-\frac{\kappa_{\text{m}}}{\kappa _{\text{c}}}+\frac{\left[1\right]}{\kappa_{\text{c}}}\right)\left(\left[S_{t} \right]-\left[S_{0}\right]\right)\right\}\) & (2) \\ NCI & \(t=-\frac{1}{\
u_{max}}\left\{K_{\text{m}}\left(\frac{\left[S_{0}\right]}{ \kappa_{\text{c}}}+\frac{\left[1\right]}{K_{\text{c}}}+1\right)ln\frac{\left[S_{ 0}\right]}{\left[S_{0}\right]}+\left(1-\frac{\kappa_{\text{m}}}{K_{\text{c} }}+\frac{\left[1\right]}{K_{\text{c}}}\right)\left(\left[S_{t}\right]-\left[S_{ 0}\right]\right)-\frac{1}{2K_{\text{c}}}\left(\left[S_{t}\right]^{2}-\left[S_{ 0}\right]^{2}\right)\right\}\) & (3) \\ UCI & \(t=-\frac{1}{\
u_{max}}\left\{K_{\text{m}}ln\left[\frac{S_{0}}{\kappa_{\text{ c}}}\right]+\left(1+\frac{\left[S_{0}\right]}{K_{\text{m}}}+\frac{\left[1 \right]}{K_{\text{m}}}\right)\left(\left[S_{t}\right]-\left[S_{0}\right] \right)-\frac{1}{2K_{\text{m}}}\left(\left[S_{t}\right]^{2}-\left[S_{0}\right] ^{2}\right)\right\}\) & (4) \\ MI & \(t=-\frac{1}{\
u_{max}}\left\{K_{\text{m}}\left(\frac{\left[S_{0}\right]}{K_{ \text{c}}}+\frac{\left[1\right]}{K_{\text{c}}}+1\right)ln\frac{\left[S_{0} \right]}{\left[S_{0}\right]}+\left(1-\frac{\kappa_{\text{m}}}{K_{\text{c}}}+ \frac{\left[S_{0}\right]}{K_{\text{c}}}+\frac{\left[1\right]}{K_{\text{m}}} \right)\left(\left[S_{t}\right]-\left[S_{0}\right]\right)-\frac{1}{2K_{\text{m }}}\left(\left[S_{t}\right]^{2}-\left[S_{0}\right]^{2}\right)\right\}\) & (5) \\ \hline \hline \end{tabular}  
* WI—without inhibition; CI—competitive inhibition; NCI—noncompetitive inhibition; UCI—uncompetitech inhibition; MI—mixed inhibition.  
\end{table}
Table 1: Integrated Michaelis–Menten equations obtained from the model explained in Figure 1, assuming product inhibition [10].